I'd much rather go eagle, par than birdie, birdie. I did go birdie, birdie once last season, though, and it was a lot of fun.
Think missing that putt that would've made it eagle, birdie was bad? The last time I had a really, really good look at eagle (about a 14-foot putt that broke left maybe 4 inches at most) I ran the putt 4 feet by and missed the birdie putt coming back, for a smooth 3-putt par.
Oh, and for people that have had eagles on par 4s by holing out from the fairway, I'm jealous. That has NEVER happened for me. Ever. All my eagles have come on par 5s, and almost all of them by way of putts, although I think I did chip in from the greenside for eagle once.