Battle wise its a tough decision. I played a Vanguard so if the enemy had Shields or Armor, it was more appropriate to use my Squad's abilities.
James has that very nice Carnage Ability, but his recharge time was slow (which may have been the way I had set him up...or Fortification).
Garrus is just so damn deadly with a Sniper Rifle, I remember him almost killing a lot of the enemies in one shot when I first got him, and continue to do really well the rest of the game.
Ashley was useless to me, and I didn't find her abilities outside of Grenades all that impressive.
Javik was strong, but I was already a Vanguard so I didn't see the particular need to take him.
Liara had nice abilities, but she went down a bit too often for my tastes.
Tali is really nice with Energy Drain(although since I get that as a Bonus Power it kind of diminishes her a bit) and has those Drones, but I can't exactly remember them being too overly useful (then again, I only used Tali on like 4 missions, 3 of those being Geth so I was mostly using AI hacking).
Can't speak for Kaidan since he wasn't in my playthrough.
EDI was super useful to me though. She has both Overload and Incinerate. I find that she is really good with SMGs, and her Decoy power usually has the enemy distracted so she won't go down as easily. The only problem I have is that since she has Overload and Incinerate, I can't really use them in succession too much.
Party Banter wise or personality wise? Liara, Tali, and Garrus are definitely up there. Especially surprised Garrus has so many lines despite being an optional party member. I like some of the stuff Javik has to say, even though I kind of hate his guts. While I romanced Ashley in the first game, I did Tali for the rest of the series. Maybe because of that, Ash had almost nothing worthwhile to say. Ended up liking James a lot in this game. I mean, I didn't hate him before the game came out, but I pretty much like everything about the guy. EDI of course, was super hilarious, and I enjoyed a lot of her questions about Humanity.
While I like the smaller squad this time around (in ME2 I ended up never really using like half the squad, especially the later people like Thane or Samara), I always end up conflicted. I try and think, "Hmm...which combination gets me the best banter" because they improved upon it so much this game. But then I realize I have to balance out my party and it leaves me pulled in two directions.
But if I had to choose, it'll probably be Garrus. Forever a Bromance!