I've run this game many more times through postgame and I have minor refinements to make to my tier list from over three years ago. As before, Pokemon within tiers are ordered alphabetically.
S [Easy Mode]
(The best mixed attacker in the game)
(The most offensively efficient Pokemon in the game)
(The second most offensively efficient Pokemon in the game)
A [Best Picks]
(A bulkier mixed attacker Typhlosion, with the drawback of being a mid-game pickup with slow EXP growth)
(The best Electric-type, but slow enough to be occasionally noticeable)
(The best physical attacker in the game prior to the Realgam Gauntlet, but prefers a 5-Pokemon team prior to its integration)
(The best Fighting-type until Heracross is obtained with fast EXP growth)
(A faster Ampharos, with the drawback of being a mid-game pickup with slow EXP growth)
(The best Pokemon in the game under sun, but requires a Fire-type teammate on the field to function at this level)
(A bulkier non-mixed Feraligatr, with the drawback of being a mid-game pickup with slow EXP growth)
(The most offensively efficient Earthquake user in the game and a Ground immune, but requires a Time Flute + 2 Rare Candies + TM 26)
B [Second Picks]
(The second best Grass-type that is less dependent on Sun to function, but the worst Phenac starter pick)
(In competition with Hariyama and Heracross, and reliant on HJK to function, but a strong glass cannon)
(The best Pokemon in the game, but can only be used for the postgame)
(A worse Flygon that is obtained earlier, gets Dragon Dance, and has fast EXP growth)
(Absurdly strong and diverse Sand setter and Earthquake user, but can only be used for the postgame)
(Damage sponge that is very hard for the AI to KO, but has poor offensive efficiency)
C [Temporary or Niche Picks]
(A notable temporary pick for the early-game and has a unique niche with Follow Me and Helping Hand, but bad otherwise)
(The strongest Intimidate user with a powerful TM movepool, but is noticeably slow)
(A notable temporary pick for the mid-game due to Intimidate and good effective bulk)
(A strong Fire-type that can be used instead of Typhlosion or Entei, but only for the postgame)
(A notable temporary pick for the early-game due to its matchup against Mirror B. and Dakim)
(A niche pick for Body Slam spam, but only for the postgame)
(A notable temporary pick for the early-game due to having STAB Shadow Ball, but falls off into late game)
(In steep competition with Ampharos and Raikou, and comes extremely under leveled, but has a niche with AI manipulation)
(In steep competition with Water-types and Earthquakers due to being very slow and vulnerable to grass attacks, but doesn't need TM 26)
(A notable pick for a rain team, but has to wait until obtaining Sludge Bomb and Shadow Ball to be effective)
(In steep competition with Water-types and comes under-leveled, but has a niche with powerful fire attacks)
(A niche pick as a mediocre combination of Intimidate, Sleep spam, and flinch spam)
(Physical damage sponge and Ground Immune, but can only be used for the final gauntlet and postgame)
D [Bad Picks]
(Gets Baton Pass but can't do anything notable with it and its only good moves are from TMs)
(It's traits are too lackluster to justify its low Speed)
(Can't actually make good use of it's Attack stat or Swords Dance and is outclassed by other physical attackers)
(Has Glare, but doesn't do anything else)
(Outclassed by Flygon and not notable as a sand team pick either)
(A good Pokemon, but too offensively inefficient)
(Outclassed by Umbreon aside from its Ground immune)
(Outclassed as a ground immune and as a sleep spreader)
(Slow with a bad movepool)
(Outclassed by other Fire-types)
(Effectively has unusable STABs and is outclassed by other physical attackers)
(Slow with too many common weaknesses)
(Outclassed by other Grass-types)
(Outclassed by other Grass-types)
(A good Pokemon, but comes under-leveled and isn't worth grinding for only the final battles of the game)
E [Challenge Run or Final Snags]
(Has no notable traits and is cursed by a lack of usable STABs, low offensive efficiency, and vulnerable defensive typing)
(Extremely difficult to use between its comically shallow movepool, low offensive efficiency, and vulnerable defensive typing)
(Comes under-leveled right at the end of the game)
(Ironically has a neigh-unusable movepool and comes under-leveled at the end of the game)
(Obtained at the end of the game)
(Overlaps many poor traits and has to rely on TMs for any usable moves)