03's beginning was preferable only in some aspects. Like, they showed certain things more elaborately like Ed and Al's backstory, their childhood, Trisha's illness and her last words along with her dying moment, that major incident in their life where they tried to transmute their dead mother back to life and in the process lost their bodies (Ed partly and Al fully) and the consequences of that incident like Winry and Pinako treating Ed, like applying bandages to his wounds, and later on they are also seen fixing the automail arm and leg onto his body, which was better. Though I'll still say that solely that major alchemical incident was done and shown better in Brotherhood, we can see there Ed's confrontation with the Truth, where the Truth literally talks with Ed. Truth's words to Ed basically gives us a mysterious enigmatic feeling about what kind of an entity Truth be. But in 03, Truth isn't presented as an entity who talks, basically entirely what's behind the Gate is represented as "The Truth" here, so that mysterious and enigmatic feeling about Truth the viewers got in Brotherhood doesn't exist here. Plus, when the incident was shown in Brotherhood, we got see what happened there fully upto when Ed sacrifices his arm to bring back Al's soul; however in 03, when the incident was shown first time, due to Al being the narrator there, the moment Al's body in taken away, a blackout happens with things then shifting to the moment when Al regains consciousness with his soul being bonded into the suit of armor, seeing Ed severely wounded like that fashion, so we don't get to see the moment there where Ed transmutes Al's soul onto the suit of armor via drawing an alchemical seal with his own blood. Due to that, the emotional weight of that incident in Brotherhood is just way more, since we basically there get to see Ed screaming and wailing in agony for his younger brother, yelling that Al is the only part of family he has left and he wants him back at any cost, even at the cost of his life, it pretty much signifies Ed amd Al amazingly strong and deep brotherly relationship, they unparalleled dynamic and genuine care for each other, and how much literally both of them are willing to sacrifice for sake of each other, serving as a testimony to their brotherly bond at such an early point of the series, which helps the viewers get invested into both of their characters all that much more.
03 also showed Ed's way to becoming a reputed state alchemist more elaborately, like firstly the fight on the train, and then Ed's alchemy exam in order to qualify for the military as a state alchemist, and then some heroic acts one after another as a state alchemist which made him more reputed and famous.
But there were certain problems clearly evident even there: 03 had two meaningless and horrible fillers in episode 4 and episode 10, showing off Ed's acts of heroism as a state alchemist, which had literally no bearing and impact on the plot whatsoever, nor were those episodes interesting literally in any way even as fillers, they totally lacked the excitement and the intriguing factor that pretty much every episode of Brotherhood had. The Clara/Psiren episode, a.k.a. episode 10 just takes the cake among those: that episode was actually so much boring that I swear that it's even comparable with the crappy SM fillers in Pokemon, even the fights in that episode between Ed and Psiren were done in such a way that they lacked any tension and the feeling of a tight situation.
Brotherhood certainly didn't have any episodes as horrible as those two (episodes 4 and 10). Those two underwhelming episodes take away a lot of points from 03's beginning as they basically showed that 03 was doing some needless and excessive plodding at the beginning sometimes trying to set up the whole thing, shortly in some parts they were extending the beginning way too much.
The Barry the Chopper episode was quite good, the imposter Elric brothers two-parter episodes were fine as well, the episode showing Yoki's backstory was...well, decent, but still, those two extremely underwhelming fillers do in fact take away a lot of credit away of 03's beginning, it basically just makes it clear that chose to extend and stretch the beginning way too much, in the process making it quite late in fact to get into the main scheme of things, going deep into the plot, which Brotherhood on the other hand got really deep into the plot much earlier without any needless plodding like 03 did via episode 4 and episode 10, which arguably helps the viewers get even more hooked into and invested in the show a lot earlier. Sure seeing Ed and Al's backstory and how they gradually got into the military helps the viewers get invested in their characters a lot as well, but seeing the plot thicken and the show getting deeper and deeper into a thick, elaborate and grand plot, resulting in a trigger of turn of events (which are all integrally relevant) one after another is basically what arguably gets the viewers more hooked and drawn into the scheme of things in the show as a whole, or at the very least that was what basically happened with me.
As Brotherhood progresses from the beginning to the middle part of the show, the plot thickens and thickens and thickens, things get very deep into the plot, events after events which are really notable, impactful both in terms of emotional weight, character interactions and intense, epic action moments, and most importantly, really very integral to the plot, start happening one after another, drawing the viewers into the grand scheme of things much more effectively compared to what 03 does. To analyze how subtly Brotherhood triggered the turn of (majorly impactful and notable) incidents one after other as it went from the beginning to the middle part, as it gradually thickened the plot let's take a look:
We have have Ed and Al's meeting with Izumi at first where we get to know everything about how Ed and Al gradually learned alchemy overcoming plenty of hardships and jams under the strict supervision of their teacher alongside getting to know Izumi's backstory as well (how she committed the taboo in order to transmute her dead child back to life and lost part over her interiors), and then things suddenly (but still subtly in a connected manner) shift to Ed and Al's confrontation with Greed and his sidekick chimeras, an powerful exciting scuttle between Ed and Greed and then afterwards Bradley's cool antagonistic brutal badassery take place with him brutalizing Greed and his chimeras. After that, we have the Xing characters (Ling, Fun and Lan Fan) introduced and pretty much immediately get to see a lot of moments which gets us invested into them in an instant, we get a good taste of Ling's courageousness, determination and her strong dynamic with Lan Fan in their fight with Bradley where Lan Fan sacrifices her arm in order to keep the prince of her clan safe, so that Bradley can't keep track of Ling anymore via the dripping blood and Ling on the other hand, being determined to save Lan Fan too even when she was nothing more than an injured baggage to him...hard to not get invested into Ling and Lan Fan's characters and like them after seeing all those incidents. And almost alongside that too, we have Ed and Al's second confrontation with Scar where incidents of immense emotional appeal and weight take place, we fully get to see Scar's backstory, and Winry's backstory too...it's revealed that Scar killed Winry's parents and Ed accidentally reveals it in front of Winry, which leads to subsequently some really touching and impactful moments which appeals emotionally in a incredibly strong manner to the viewers; it really hard not to genuinely feel deeply for Winry at the point when she picks up a pistol nearly and takes aim ar Scar, the murderer of her own parents, but...still for some reason can't shoot. She has an emotional breakdown after some time, bursting into a flood of tears due to not being able to shoot the killer of his parents, when Ed consoles Winry in a deeply touching and caring manner, making her realize that the only reason she couldn't was that because that was the genuine nature of her and her parents, they were meant to just give life and not take, her parents treated and saved the lives of many Ishvalans who were the sheer enemies of them Amestrians at that point, she herself gave Ed one arm and a leg and gave him a new life and in the end, promises to never makes her cry again, and even if he does, the next time she cries, it'll be tears of joy. Those deeply touching and caring words of Ed towards Winry severs as a testament to how much incredibly and amazingly strong Ed-Winry dynamic, which showed how genuinely and deeply they actually did care for each other; overall it was a subtle and masterful representation of emotional appeal and impact via deep character backstories and wonderful interactions. That also showed that how subtly Brotherhood actually could move on from epic and intense action/fights to suddenly really strong amd touching emotional appeal and interactions.
The aspect of depicting the turn of events, with all those events being being really impactful, notable in terms of intense action, wonderful character interactions, unveiling deep character backstories and making a strong appeal emotionally, and most important of all, being integrally relevant and important to the plot, whilst gradually going deeper and deeper into the plot, is what Brotherhood did masterfully: with the trigger of the turn of events starting to happen, each of those important, notable and major incidents while happening one after another feel so much connected with each other. It doesn't feel like we are randomly leaping from one major incident to another, they are so integrally connected with each other and the plot that while witnessing the turn of events, it feels like we are watching a real compact and plot heavy anime, where almost everything/almost everything feels really worthwhile and really important plot wise. We are moving from one major incident from another, with literally each and every incident feeling amazingly connected to each other, integrally important and relevant as well in the plot.
This compactness and the integral connection with one major important event to another is something which is very much felt like missing in 03, and certain events in between feel not all that much important, a bit stretched and unnecessary as we move on from the beginning to the middle part in 03, due to some extra stretching and plodding at the beginning, which makes certain events feel quite a bit random and a bit unnecessary, which makes it feel like the compactness and the integral connection from one major/impactful event to another which Brotherhood has, in very much missing here, a.k.a. in 03. Almost every event doesn't feel as integrally important and worthwhile plot wise like Brotherhood (which by an expect actually pretty clear illustrates the shher different in quality in the construction of the two shows and how much better constructed a show Brotherhood is compared to 03).