I doubt it's just me, maybe it is, but I doubt it. When I shave with my electric razor at work I almost always shave my neck and the sides of my face first, leaving the obligatory goatee, one of which I had for a few years. Then I'll shave my chin, leaving a mustache, which gets shaved off last. Sometimes I'll shave the mustache first, leaving a chin-only goatee.
I think I look good with a goatee, a little hard even, especially with my old goatee which at its longest made me look a little like Jim "The Anvil" Neidhart. Pictures are not currently available :P
I don't think I look so good with a mustache.