Bishops vs knights
This is a recent online game (3 days/move) I played, in which it is very clear how a battle between bishops and knights can be central to a game.
In the position below, my opponent just played e3, which allows me to force a trade of knight for bishop. Since the option arose so early, I felt this could be a good imbalance to work with. Throughout the game, my strategy became centered around trying to activate my bishops and make them better than his minor pieces.
After the trades on e5, my g7-bishop became constrained, but as it turned out, I was given the opportunity to open up the position and give my bishop a good diagonal to work with. And at the same time, I won a few pawns.
In the position below, the e5 pawn is actually vulnerable. It seems to be well defended by the f-pawn and the queen, but this is all just an illusion. The f-pawn is easily diverted with g5. The knight is short on squares, which forces the f-pawn to capture on g5 and give up protection over e5. Since the queen also attacks e5, the bishop is protected as soon as it captures the e5-pawn.
I managed to open up the position, and my bishops are better than his minor pieces, just as I had aimed for. However, the decisive blow was a major blunder from my opponent.