Lots of things can go wrong with a plane. Not very often, but when we're talking about the very small incidence of bad things happening, a lot of the time, we're talking about things completely separate from engine failure.

Maintenance has a lot to do with many accidents, and I would think that flying a newer plane would minimize this concern to a certain extent, although that might be irrational thinking as well.

Regardless, I think when comparing the 777 and 747, generally 777s are just better planes; they may not look as grand, or even as safe, since when the paint jobs are equal, 4 engines certainly looks better than 2. But on the whole, flying a 777 means flying a newer better-built machine, and that certainly takes care of any preference I might have otherwise to having more engines.

As noted elsewhere in the thread, the 777 (knock on wood) has at this point never been involved in a fatal crash.