Magic
Bartimaeus has an incredibly good memory, as he can shapeshift into someone after a single glance. He has trouble shapeshifting into detailed smaller things (as demonstrated when he attempted to shapeshift into a Fingerling), and can't shapeshift into subcellular things.
He also cannot shapeshift into large things such as dragons without a really large amount of magic.
Unlike Alucard, his teleportation skills aren't limited. Alucard's teleportation is only limited because he actually needs Bartimaeus to do so, and that he has phasing access to the Other Place.
Aside from shapeshifting into other creatures, he can take the form as objects and plants too. He can shapeshift into the magic sword 'Voidcrosser' which Alucard uses at times.
Personality
Bartimaeus is often humorous and extroverted, quite unlike Alucard who rarely jokes around and is very secretive. Despite his extrovertedness, he keeps his and Alucard's secrets to themselves and will often remind Alucard to keep quiet. He and Alucard share a faint master-servant relationship alongside their partnership, as Alucard often tells Bartimaeus to bring him his wine or to haul stuff from his storage vault in an IRIS complex.
He has been with Alucard for most of Alucard's life, and can form major synergy with their attacks when combined. Their partnership is mutual, as Bartimaeus needs Alucard to enter the material world and Alucard needs Bartimaeus to perform many of his powerful attacks (eg. the inferno, the surge, and others).
TLDR; Bartimaeus has trouble shapeshifting into tiny things and larger things, and is humorous and extroverted except when it comes to Alucard's secrets.