Well here's a complete breakdown on all of the legendaries and their impact on competitive battling:
Articuno: First, it has a 4x Stealth Rock weakness. Second, it has no moves, especially since Sheer Cold is banned. At best it can SubRoost. All you need to worry about are Ice and Flying attacks.
Zapdos: A pretty solid mon, but not overpowered. You usually have a good idea what kind of attacks it will have. Tyranitar stops it well, you can force it out for SR damage, and a good fraction of sweepers carry Rock or Ice attacks.
Moltress: 4x SR weakness again. Fairly shallow movepool. Volcarona is a better choice. Can still be useful in lower tiers though.
Mewtwo: I'm not going to argue against this one. 110/154/130 offenses with 106/90/90 defenses. Also really good movepool.
Mew: 100x6 stats aren't what they used to be. Base 100 speed only ties with most legendaries these days. You want a Nasty Plot Sweeper? Zoroark and Azelf do that with better stats. You want a support wall? Chansey/Blissey do that better. Baton Pass? Smeargle can have Spore and Shell Smash/Quiver Dance. Its typing makes killing it not too difficult.
Raikou: Good special Sweeper, but not the widest movepool and Earthquake's pretty much a OHKO
Entei: Pretty small movepool for a physical sweeper, and Arcanine has access to Fighting, Electric, and Ground moves with more useful abilities.
Suicune: Suicune is better as a wall, which means Taunt is a problem for the classic CroCune sets. Ferrothorn, Blissey, and anyone with Water Absorb/Storm Drain pretty much make it worthless.
Ho-Oh: Basically a Moltress that's actually good. Brave Bird and Sacred Fires off of a base 130 attack? And 106/90/154 defenses? Yeah, that's bannable.
Lugia: Some of the best defenses in the game, and it has Roost. Yeah it's understandable that it's uber.
Celebi: IIRC Grass/Psychic is the type combo with the most weaknesses. If you don't have something on your team with an attack that OHKOs Celebi something's wrong with your teambuilding. Also struggles to take down Dragons.
Regice: Mono-Ice typing is terrible defensively. And it has base 50 speed. Easy kill.
Registeel: This one has better defenses, more resistances, and can use Curse well enough. Still easy prey to an Earthquake, Close Combat, or a few Flamethrowers though.
Regirock: If you don't have anyone with a Water, Steel, Fighting, Ground, or Grass attack on your team, you probably should go back to the drawing board with your team
Latios: Not that bad without Soul Dew. You can Pursuit or Sucker Punch it, especially since many versions are choiced. Gengar also speed ties non-scarfed ones.
Latias: I actually find this one more annoying. But it still has trouble with Scizor, Tar, Blissey, etc.
Groudon: Uber, 'nuff said
Kyogre: The most popular uber for good reason. Autorain, Water Spout, and Thunder....next please
Rayquaza: Base 150 attacks + DD+Extremespeed? It might be uber
Jirachi: another base 100X6, but with a super-awesome ability. However, it's still checked by Ground types, Heatran, Volcarona, Scarftom-W, Magnezone...
Deoxys: Normal and Attack versions are def. uber. Speed, however, us usually used for support and is on the frail side. Defense is awesome if used correctly, but it's also setup fodder for DDers and Volcarona, and Scizor laughs at it.
Azelf: Solid offenses and a decent lead, but pretty much OHKOed by Pursuit/Sucker Punch or some neutral attacks.
Uxie: More of a defensive utility mon. Unlikely that it will OHKO you.
Mespirit: The worst of the trio. Bad speed that lets it get KOed by many sweepers
Dialga: Uber and only Dragon IIRC that isn't weak to Dragon
Palkia: Yep. Only one weakness and better speed.
Giratina: My favorite uber. Has over 500 HP at max. Next...
Cresselia: Not an offensive threat unless it gets a ton of CMs in. Also needs to worry about weather
Darkrai: Nobody likes 80% accurate sleep moves from a base 125 speed mon = ubers
Manaphy: It has a move that offers +3 SA, plus good defenses and instant Rest awakening with Hydration. It would definitely not be OU this generation.
Phione: It's just a base 80X6 mon without Tail Glow. Nothing to fear
Heatran: I kinda feel like this one was meant to not be a legendary in the storyline, similar to Volcarona. While it can be annoying, it fear Water, Earthquakes, Fighting moves, and furthermore only has base 77 speed.
Regigigas: You have 5 turns to take pot shots at it.
Shaymin: Shaymin-S is understandably uber, but normal Shaymin is outclasses by Ferrothorn and Celebi (although Seed Flare can be fun). Also has a decent number of weaknesses.
Arceus: Don't go there.
Victini: Fairly easy to check just like other Fire types.
Cobalion: Outclassed by Lucario and has no moves
Terrakion: A double-edged sword. Its typing is great offensively and bad defensively. Good speed, but that doesn't matter when there's Bullet Punches/Mach Punches/Aqua Jets to fear.
Virizion: Good for anti-weather, but has to worry about Psychics, Fire, Ice, and Flying
Tornadus: Understandably the inferior one in the trio. Relies heavily on Hurricane and frail.
Thundurus: Already voted uber; basically a frailer yet faster Zapdos with Nasty Plot
Landorus: Not much to worry about. Basically a more offensive Gliscor without Poison Heal.
Reshiram: Uber
Zekrom: Uber
Kyurem: Remember what I said about Regice? Well here it is again. While it has great offensive stats, its physical attack goes wasted. Bullet Punches and Mach Punches easily puts it in its place. Also weather-reliant for max Blizzard spam.
Going to skip Keldeo, Meklotta, and Genesect because they don't exist yet.
Furthermore, a breakdown of legendaries by tier:
Uber: Arceus, Darkrai, Deoxys (A), Dialga, Palkia, Giratina, Kyogre, Groudon, Lugia, Zekrom, Reshiram, Ho-Oh, Manaphy, Mewtwo, Rayquaza, Shaymin-S, Thundurus
OU: Terrakion, Celebi, Virizion, Jirachi, Lati@s, Heatran, Deoxys-S, Landorus
BL: Kyurem
UU: Azelf, Cobalion, Cresselia, Deoxys-D, Mew, Raikou, Registeel, Suicune, Tornadus, Victini, Zapdos, Shaymin
RU: Entei, Moltress, Uxie
NU: Articuno, Phione, Regice, Regirock, Regigigas, Mespirit
And non-legendaries in Ubers:
Blaziken
Garchomp,
Excadrill
Wobbufett and Wynaut*
Smeargle, Bidoof, and Octillery**
Ludicolo, Kingdra, Kabutops, Magikarp, Mantine...***
*=While not banned this generation, these two were banned in Gen III & IV thanks to Shadow Tag + Encore
**=All of these have access to the ability Moody, which is so broken it's even banned in Ubers. It allows a Bidoof to take down an Arceus with enough luck
***=These guys got Swift Swim, which means that in all tiers below Ubers you cannot use then in conjunction with a Drizzler on your team. The combo is legal in ubers though.