7...Bxc3 is not that horrible, but a bit passive: anyway, you could postpone that exchange until White castles, since he probably won't dare to avoid the doubled pawns with Bd2.
However, after 7...Bxc3 8.bxc3, I don't agree that 8...d5 is "the normal continuation" at all. After 9.ed5 cd5 10.Ba3, Black won't be able to castle and faces huge difficulties. When you surrender the bishop pair, you better place your central pawns on squares the opposite colour from your remaining bishop; also, you don't want to open the game too fast.
8...0-0 is logical, avoiding all that Ba3-nonsense. 9.e5 Re8 is not to be feared, and Black will develop solidly with ...d6, ...Re8, ...c5 and ...Bb7 (or ...Bd7-c6), trying to put pressure on e4, since he has no way of attacking the weakened pawns on the queenside (a2, c2, c3).
White's plan is more active. He can support his Pe4 and prepare a breakthrough with e4-e5. His plan may go 0-0, Bg5 (in case of ...h6, go back to h4, don't exchange), Qd2 (or Qf3-g3), Rae1, f4 and e5, opening files and diagonals. Alternatively, he may engineer e4-e5 without f2-f4, with support by the bishop from f4 or g3.
Note than the Bg5-Nf6-Qd8 pin is especially annoying since Black has no dark square bishop to break it, and damaging your king's shelter with ...g7-g5 or ...gf6 is not really what you want to do.
All in all, White has a small but clear advantage, and Black has a solid but passive position.