My usual middlegame strategy is to gain an advantage, however small (say a pawn), and convert it to a win in the endgame. I position my pieces and plan attacks accordingly, so that I can grab the small advantage I need. I don't actively hunt for the opponent's king, and prefer to first gain an advantage, so I can exchange pieces and win. So the entire game grinds on.
That said, I don't (usually) miss a checkmate if my opponent blunders in the middlegame. On the whole, though, I prefer taking the game to the endgame, even if my advantage is significant (~3 points).
However, I've seen players who actively attack the king in the middlegame itself. They position their pieces in such a manner that they threaten checkmate, and seem to plan to finish up the game in the middlegame. They try to take advantage of the castled king's reduced mobility, and checkmate him. The success of this strategy depends, it seems (based on what I've seen), on both the opponent's skill level as well as on luck.
I wonder, as a general rule, what should one's middlegame strategy be: should one actively hunt the opponent's king in the middlegame itself, looking for a checkmate, or try to gain an advantage which can be converted to a victory later?