Would the Battle Sorcerer variant be a Tier 2 class like the Regular Sorcerer or a Tier 3 Class do the limited spells known?
In general, any class with 9th level spell progression and a flexible spells known list (basically any class that lets you pick two or more spells known/class level, so Beguiler and Dread Necromancer wouldn't count) is considered Tier 2 material. The exceptions are home brew.
Classes with a set spell list and limited access to learning new ones are usually Tier 3 (Dread Necro, Beguiler) or lower (Warmage, Healer).
Edit: Improved BAB isn't worth that many spells known. TT is a single 6th level spell, Shapechange can give Full BAB, and Divine Power is granted by at least two Domains (so Arcane Disciple)