Myself (and I've done a few of these) I actually do them simultaneously. I tend to cut FX during the day, then work on Composition at night - Or I'll do one day of FX, one day of Music, etc. However I tend to start with FX either way - but YMMV..
One thing I always do, is have a spotting session/long discussion with the filmmaker about where things are going to go, and what overarching concepts are happening with both Sound and Music. The good thing about this is both the Sound and Music departments are always in that session! :) Since I'm doing both, I have a fair idea when one is going to be dominant over the other, and generally avoid conflicts - although there's always a director's prerogative to change his mind! :)
The downside is of course, that's it ONLY you, and so if you run low on inspiration, there's no other co-creator to kick your a$$!
Of course these are generally indie projects, where the director/producer can give me the time I need to work on both elements...