Myspace is blocked from work, so I can't comment on the recording for the tibe being. That said...
If you're playing a Mesa F-50 and you're not happy with the sound you're getting recorded even though you love it live, then there's something wrong with your micing technique or the way you're dialing in your amp. Period. That's a totally pro setup, there's no reason you shouldn't get a fundamentally solid tone out of it.
Try two things here - first, dial in your amp not so it sounds good in the room, but so it sounds good from an inch or two in front of the speaker, since this is where the mic is "listening" to it. There's a WORLD of difference between a good room sound and a good close mic'd sound.
Second, spend a lot of time working on mic position. Especially with something like a SM57/58, they're really pretty position-sensitive, so lots of small adjustments are going to be in order before you really nail the position. Also, your ear will initially tend to prefer "brighter" tones as they'll seem to be a bit louder, so try dialing in your mic position, recording a few seconds, then walking away from 10 minutes. If the sound you were previously happy with sounds pretty thin and ice-picky when you come back to it, you're too close to the center of the cone. You want balance, not oodles of treble.
My experience with models has been they're SUPER-user friendly; literally a plug-and-play solution to get a good tone. However, while it's way easier to dial in, I've yet to see a modeler really produce a result as good as a properly mic'd real amp. Learning how to mic an amp has a huge learning curve (I still don't even feel like an expert), but is totally worth it once you get the hang of it.