I love this question. It's a total fanboy question. It's like asking what's better, a Glock 26 or a Glock 42? on a gun forum. They do the exact same thing, the same way, differently lol. Though I can't answer the question definitively, Steel has pointed to a study that goes straight to the question. I'll take their word for it.

I don't really have a pony in the race as I switch between my DE's, my Feather AC, and my straights often enough. I'll say this anecdotally:

Unless it's the weekend when I can devote more time, my DE is closer. At least in area's. It has to be. My beard grows sideways in the hollows of my neck. This takes a steady hand with a straight to conquer. So M-F, I just live with the ok up and down strokes vs sideways strokes needed as M-F I shave in the mornings. And I'm not good in the mornings. Of course - Not a problem with my DE. Mirror or no mirror, that thing is easy to angle and takes those hollows the way an Audi takes corners.

That said, I'll swear till the day I die that my straight shaves last longer than my DE shaves. This makes no sense whatsoever other than admitting that clearly the straight shaves cut closer. It's not like the straights steel temporarily stunts growth vs a DE's steel lol! So all said and done, I would have to say that my straights cut closer... but I don't know if they are sharper. I actually don't think they are.

The DE is VERY handy when you are busy, sharper than sin, and do the job very well - but it's never as smooth, new blade, one shave or many. My straights, short of a bad hone, are always a pleasure now that I have been doing it for so long that even in the mornings, I can shave in my half baked state.

Seriously, I'm not good in the mornings - I haven't stretched many a time with both my straight and my DE in the mornings. The above still is true.

I love em all, but I think my DE's are sharper. In spite of that, I get closer with my straights. Sharp isn't everything.