Yeah, time for a word on the BBS thing I think.
Whilst some people say that BBS stands for "baby's bottom smooth", more discerning shavers may prefer "billard ball smooth". In either case, it's a snare and a delusion, which has been responsible for more cases of razor burn than just about anything else. The idea is that you can't feel any stubble at all when you run a hand over your face, in any direction. There's a few problems with this.
Firstly, groping one's face in order to check for smoothness isn't particularly good for the skin - Tony's commented on this before now - and isn't called "faceturbation" for nothing. Give yourself an appreciative feeling up when you slap on the aftershave then leave it alone, that's my advice. Secondly, a man's face is in no way similar to either a cue ball or the quieter end of an infant in the usual run of things, and if it feels that smooth it's a racing certainty that it won't stay that way for long.
And finally, there's the matter of what it takes to achieve this level of clean-shavenness. (You hear stories from some of the straight razor crowd about getting a BBS shave from a single pass, and I'm pretty sure that I've done it. Not 100% sure you note, because I'd probably been knocking back the absinthe at the time). Anyway ... you need a either a DE with a very sharp blade or a cut throat in excellent fettle, and a pretty slick technique; furthermore you're going to have to work against the growth (ATG) or do multiple passes across it. This is a recipe for irritation, rashes and general unpleasantness if you do it on a daily basis. Far, far better to go for a nice, comfortable shave day to day, and maybe pull the stops out for weddings, funerals and court appearances.
So, edging back towards the matter in hand: a new sharp blade will generally give a closer shave, but it'll probably be more pleasant to shave with second time around. Some blades, usually old ones, deteriorate gracefully and will give you half a dozen good shaves, whilst others die suddenly and become horrible to use mid shave. Feathers are an example of the latter in my experience, a real 2 1/2 day blade.
Ergo: if you really want your face to be like a billiard ball, use a two day old blade or a cut throat which has been stropped a few times to get those demons out of it. Either way: cultivate a very light touch.