-The Birds in R/G/B/Y/Fr/Lg were the easiest ever. Zapdos just had a small labyrinth that you could get through easily, Articuno had a small puzzle that you complete without even realizing. Moltres was just dropping through a hole, which also was too easy.
-The Birds in XD was also very easy. If you captured XD001, this is seriously a joke. The only thing that may have ruined it was if you ran out of Ultra Balls or if you ran out of Potions. And even if you fainted them, you could always come back to try them again. You simply could not not capture them. The only difficulty with them was that you fought two at the same time and could only throw one Ultra Ball in one turn.
-The Beasts (every time someone calls them dogs my brain implodes. Seriously, just look at Entei and Raikou and dare to say that again) in G/S were alot harder. You had too fully explore the Burnt Tower with a Pokémon with Rock Smash. And seriously, who had a Pokémon with Rock Smash in that time that wasn't specifically for this reason. After that, you had to encounter them in the wild. You needed luck for that. After that, you had chase them across Johto. And that was WAY harder then chasing Lati@s. After that, you had to weaken them a bit without fainting them after which they ran away and you had to chase them again. Unlike with Lati@s, you couldn't use Shadow Tag or Mean Look on them because Shadow Tag didn't exist then and they had Roar. After weaking them enough and finding them again, you had to put them to sleep (Sleep Powder missed. Wild Raikou ran.). If that worked, you had to throw Ultra/Fast Balls at them. If they woke up before you caught them, you had to chase them again. After catching one, you had to repeat the process again two more times. And since there were three, you couldn't use the Master Ball.
-The Beasts in Crystal. The Burnt Tower was now part of the main story line and you didn't need Rock Smash for it. After that, Entei and Raikou were the same as before. But you encountered Suicune after beating the Wise Trio in the Tin Tower. It didn't run away, which made catching Suicune much easier.
-The Beast in Colloseum. This was pure hell for the following reasons:
1. The had Shadow Rush (Colloseum version), meaing that they had recoil damage. After finally bringing them down to the red, they kill themselfs.
2. You had to beat four Pokémon of a trainer with incredable strategies and combinations, like Earthquake/Protect and Water/Flying/Lightning Rod, in a double battle.
3. After the Beasts were brought into the fight, you still had one more Pokémon to beat. And while you focus all your strenght on that single Pokémon, the Beast kills off your Pokémon one by one.
4. Entei had partner Pokémon with Earthquake.
5. You could only throw one Pokéball per turn, while you had two Pokémon to give orders to.
The biggest difficulty for this one was that you had to beat a very strong trainer and snag an extremely difficult Pokémon to capture at the same time. And beleive me, that was pure hell.
If you fainted them and saved afterwards, they weren't gone forever, but they only appeared again untill near the end of the game. And that was a long time away. And if you missed them again at that point, you could still meet them in Deep Colloseum. But beating a trainer with lvl. 60+ Pokémon while trying to prevent a legendary from fainting and trying to catch it, isn't really that easy as it seems. And depending on the Beast, you had to go through 2-4 rounds with four trainers each.
-The Beast trio in Fr/Lg were also very difficult. They were the exact same as Lati@s to catch, except for one major aspect: Entei and Raikou had Roar. And if they used Roar, they were gone forever. So once they used Roar, they couldn't be used again. Because of that, you couldn't trap them with Shadow Tag, etc. and it is much more difficult to chase the Beast in Kanto then Lati@s in Hoenn, but still less difficult then in Johto.
-The Regi trio in R/S/E were near impossible to do if you didn't have a guide and if you didn't knew braille, but if you did have a guide or knew braille, this was very easy. And IIRC, inside that tiny book that you had received together with the game, there was the braille alphabet and what letter they were in our alphabet. So that really wasn't all that difficult.
As you can see, the Beasts were most difficult to get to, were most difficult to fight and were most difficult to catch. And in Colloseum the method of capturing them was absolutally horyfying.
So the Beast Trio gets my vote.