First of all, I would like to say that I am not explaining why the other "starter birds" are better; simply why Talonflame is not as good as it seems. Secondly, I am probably not going to reply to the comments here for several reasons. Most of what I state here is factual, and not opinion-based.
-Talonflame's design is not as creative as that of the other "starter birds"; this is an image of a shikra: http://upload.wikimedia.org/wikipedia/commons/f/fe/Shikra_(Female)_at_Hodal_I_IMG_9156.jpg. Talonflame looks almost exactly like it in several ways.
-Talonflame's name is literally two words fused together, which is unusual for a Pokémon name nowadays. Much better names could have been "Fletchyro" (Fletchling + Pyro) or "Fletchipiter" (Fletchling + Accipiter; the name of the sparrowhawk genus).
-Talonflame is apparently well-liked for its Hidden Ability known as Gale Wings, which provides priority to Flying-Type moves. While this is useful, it does not help Talonflame when it comes to defences, and because this is a Hidden Ability, acquiring a Talonflame with the ability is not easy. As for its natural Ability (Flame Body), many of the moves that are likely to defeat it (those of the Water, Rock and Electric-Types) will not involve contact, so the likelihood of an opponent of an advantageous type becoming burned without the cause of an attack is significantly decreased.
-Gale Wings can be negated by Gastro Acid.
-Talonflame has a quadrupled weakness to Rock-Type moves. Even though it loses its weakness to Ice-Type moves because of the fact that it is part Fire-Type, this extreme weakness to Rock-Type moves is the price for it.
-Talonflame has one immunity (Ground-Type moves), while the other "starter birds" have two (Ground and Ghost-Type moves). Also, if Gravity or Smack Down was used on a Talonflame first (provided Smack Down would not have already defeated it), Talonflame would gain a weakness to Ground-Type moves.
-Talonflame is able to learn the move Solar Beam, which is a potential threat to Water-Types. However, because this is a two-turn move, this leaves Talonflame vulnerable to an attack that could finish it off for one turn, and Talonflame does not gain a same-type-attack-bonus from the attack.
-Talonflame is able to learn the move Steel Wing, which is a potential threat to Rock-Types. However, this attack does not have perfect accuracy, and Talonflame does not gain a same-type-attack-bonus from the attack.