I was looking at my old dive knife in its trusty scabbard the other day . . .it reminded me of the time that my first stage became completely entangled in a massive blob of monofilament during a night dive. I was stuck face down on the bottom in the muck, couldn't move forward nor back nor up. Actually, wasn't even sure what the problem was at the time. An intraining DM came along and used his BFK to cut me free. The moral of this story is, that I wasn't able to reach my knife.
Then for many years I carried the snips attached to my bcd. Replaced them as each pair rusted out, unused. Haven't bought any new for a few years now.
In 20 years, there was the one event and my not so BFK was of no help to me at all. I am glad that the intraining DM had a knife, but I'll bet that one of those little line cutters would have worked just as well, if not better.
And all that said, what one carries and where, depends on where you are diving.