...weell, I thought it might get a chuckle... because in the final analysis it's makes no difference which platform you choose since (unlike many instruments, certain vintage audio gear, or even some cars) both will become as nothing with the passage of time. There, I had to explain my joke... or was it a philosophical world view? ... or perhaps it was because I owned both at one time...
Anyway, if we're getting serious here at the homerecording comedy club ladies and gentlemen, then I would have to say that, economics aside, it is a valid question. My take? Since there's really not much theroretical difference beween the two as far as audio quality is concerned, then it's all about personal preference.
I'm old school, and if I were to be in a position to have to make a choice, from scratch, with a limited budget, I'd choose the all-in-one. I guess I never transitioned well into the virtual studio world. I find 'mousing' around on a screen to be non-intuitive. I much prefer the tactile world of knobs and faders. I like the analog 'feel' of dialling in an EQ (as opposed to typing in numbers), truly performing a cross-fade (with faders!) and physically smacking the record or pause buttons. Old fashioned, I know, but there you go.
Having said that, because I'm getting back into home recording (yet again) and because I already have a board and FX and everything else, my next purchase will be another 'state of the art' computer, but I will look at it as more of a tape deck than a DAW.