I don't have a serger, so I could be biased... but I'd go with a sewing machine for more versatility. For a while all I wanted was a serger, but really, I like the look of a turned and topstitched diaper So Darn Much I don't know if I could give that up!!
(although I admit to longing for a serger when I'm making doublers... it would be *way* easier to just serge the edges than t&t the doublers and then avoid the thick edges... but I'm still happy

)
Plus, I think that sewing machines are cheaper... and easier to figure out right from the beginning (this of course only hearsay because I've never even touched a serger!)