Ok so B&K have the ap advantage but it's not that simple. Both of them share a lot of powers, but both have one or two advantages. Age has invisibility which Banjo doesn't have a real answer for while Kazooie has ice eggs that Abe doesn't resist. Overall I'm going with the bear and bird simply because their sheer AP and dura advantage can rank a hit while abe attacks them invisible and then that element of surprise is less effective next time. Meanwhile Banjo and Kazooie can land a few hits and smash him with eggs, especially ice attacks. Banjo and Kazooie with high difficulty
Banjo & Kazooie have dealt with invisibility users a few times before, so they wouldn't be hopeless against it. Their durability, healing and regeneration make it so anything that's not possession won't really affect them. A couple of grenade eggs could probably put Abe down, given they're a fair bit stronger than B&K's arsenal which is already 3.6x Abe's durability.
If abe positions himself correctly he only needs a very short amount of time to posses someone. While he does have to audibly chant this adds a time limit to how long Banjo has to take him out. Abe only needs 4-8 seconds to posses someone.
If Abe instantly uses an invis ring into climbing up a tree and abuses his range I think he could potentially pull of a possesion.
He would likely do something like this in character as well.
The thing is that Banjo also has good range with the eggs and can just chase Abe flying with Kazooie, then beak bomb him. He could also use the wonder wings to counter the possession with no problem since he has enough time to react to him and the wonder wings can even K.O. ghosts and are invunerable to all of Gruntilda's spells.