My ability to play is ranked right up there with the worst players in the world, but I have finally gotten to the point of needing more than the simplest of diatonic scales. In my attempts to play accidentals, I have found that half-holing is not dependable for me.
As a result, I have tended toward cross fingering to pull notes down a half step. While this seems more accurate, it is less intuitive. Playing a half step down by half covering a hole seems to make sense, while covering two holes below doesn't, unless you think about it...It also slows my playing considerably, but that may improve with practice.
I was wondering if other people have a preference, and why you prefer your method.