Would I get a better sound from using an interface and some kind of amp sim, or using an interface connected to a mic which sits in front of my amp, perhaps an sm57/8.

depends on your amp, the interface, your computer, the amp sim, etc.

if you have a good amp with a place to turn it up enough to get a good sound out of it, then you can get a good sound there. if youve got a crappy amp, sims are going to sound better. ive been using sims more and more these days, mostly because they are quiet. however, i find that using a real amp is often better (w/ a good amp) because you get more of a real interaction between guitar and the amp this way. but you can get a damn good sound with sims, so go with whatever you want.
Jof has got it spot on, but if your recording is inspired by the sound you get from your amp, don't fixate too much on finding that sound, I'm sure those who you may disturb can live with a few minutes of noise.

If you're looking for a sound you haven't yet heard sims are the way forward my friend .