I've sampled both LEVIATHAN and REMISSION but haven't sat down and listened to either in its entirety. I'll glady offer some babble about my opinion (preliminary as it is), but first, the usual disclaimer/reminder/blahblahblah: I speak only for myself and do not claim to be a prog expert by any means. As for the "metal" genre (prog &/or other), here's a few bullets & blurbs regarding some bands I've heard:
Tool: in my opinion, the best band of those that can be deemed "metal"
Disturbed: okay
Queens of the Stone Age: okay
Kyuss: okay-to-yawn
Metallica: okay-to-yawn
Megadeth: okay-to-yawn
Dream Theater: okay-to-yawn
Pain of Salvation: okay (so far -- not much exposure to their work)

If you're familiar with Kyuss, I'll offer this about Mastodon: their pace and rhythms are far more relentless than Kyuss. I feel Kyuss "played"& experimented with their songs more than Mastodon does -- especially with regard to pace and rhythm. I was never a fan of Kyuss (nor did I dislike them). Most of Mastodon's songs are frenetic and relentless. If you like "in your face" metal, you might just love Mastodon.

Compared with Tool? "Muscle" and tone of both bands are similar. Mastodon is equally heavy, albeit more frequently so, song after song. Tool varies their tone and pace more often than Mastodon does. Some folks prefer Tool's "simpler" music. While I can't say that Mastodon is derivative of Tool, nor would I call them Tool "wannabes," I must say that I do hear Tool's influence in Mastodon's music. Neither band's sound is "muddy" or "buried" (thankfully). However, I've yet to be overly impressed by Mastodon. Good? Yes, but Tool, on the other hand, usually drops my jaw and boggles me. Can't say the same about Mastodon, but that's definitely a subjective thing. It's obvious that Mastodon drops plenty of jaws -- hence their success and consistently good reviews. I also find Mastodon's musicianship, on an individual basis, a tad overrated. Yes, they're quite good and very capable -- certainly better than mediocre, and far from blah --  but none of them strikes me as being a great instrumentalist. If you prefer Tool's more straightforward & relentless sound, my guess is that you'd like Mastodon quite a bit.

If your idea of prog metal is more Dream Theater and Pain of Salvation (rather than Tool), then Mastodon may not be for you.

In the end, would I spend $15 on one of Mastodon's CDs?
Right now, probably not. If I had the cash lying around and felt a little more frivolous? Sure, I could easily see myself buying either LEVIATHAN or REMISSION.

Hope the above babble helped, even if only a little.
Cheers.
Dan