BP is too smart to be the leader of an African nation and side with the American government
I'm pretty sure there's two sides to Black Panther. The politician sees why he should side with Tony on this. If you agree with Batman about Superman, how could you be on Captain America's side? It's about the same thing; Unchecked power.
Also, you forget about Winter Soldier. Black Panther is obviously after him. If you notice, that scene where he's running in the tunnel and Captain America is chasing him, Black Panther is chasing Winter Soldier. Winter Soldier is frantically looking back running while Black Panther is after him.
Peopld keep saying Scarlet Witch is the most important player on Captain America's team. While that might be true, I think everyone is overlooking Ant Man. You've seen what he could do in his film versus Falcon. He also has the ability to turn into Giant Man in this film. If he can miniaturize and expand into Giant Man the same way he did in Ant Man, he's going to be a bit of a headache.
Like I've said before, with all this said, if it were an open field with no corners and so, even without Vision, Iron Man's team takes this. Black Panther himself can should be able take Captain America or Winter Soldier (definitely). If his vibranium is like the comics or cartoon, he could easily emit sound waves that will pin Scarlet Witch to the ground similar to Hawkeye's arrow in Age of Ultron. He's a master of pressure points and could bring Giant Man down as he's done (Even in Giant Man form he can still be taken down as if he were regular Ant Man). Then it's just a case of Iron Man and War Machine taking out Falcon and Hawkeye, although in an open field, Hawkeye becomes even more dangerous.
Still, this is a match of brawn vs brain and brawn (armors). There's not a single above average intellect on Captain America's team (it's not Hank Pym's Ant Man nor the intelligent version of Falcon). Chess not checkers.
Yes, it's a team full of heart, but since people are using basketball references, it's Allen Iverson and the 76ers versus the Lakers.