I seem to manage to get gyroed a lot. Plenty of legs too. Death by engine crits doesn't seem as common for me as the gyro.
In general, though, it does seem the leading cause of death is CT crits. That's more or less how mechs work, they can run around missing a fair number of pieces, but they can't operate without the engine, and losing mobility is a death sentence for lighter mechs. After that is what I'd call lucky crits. A single ammo bin can take out a mech, and pilot hits always seem to come in clusters.