I also have a triaxis and JMMP is pretty spot on. Mine is a 2.0 Recto. I never use the Recto mode, it's harsh sounding. If you look at the manual, you'll see three modes; rhythm (clean channels two sounds), ld1 three sounds, and ld2 three sounds. In lead 1, you have the in-between sounds and the recto mod. Lead 2 is all of the Mark lead tones (II, III, IV). This is the channel that everyone uses. There isn't a lot of difference between the sounds, III is a little more sizzle, II is a little thicker, and IV is in the middle. I use Petrucci's settings, III for crunch rhythms and variations between II and IV for leads.
To answer your question, it's analogue as far as the tone, but digital for the midi and patch stores, changes. So, no modeling or emulation, if that is what you are asking.
The settings are a bit strange to get used to, if you have previous amp experience. The eq is wired in series, so each one affects the other and adds gain. If you buy it, start with 5 treble, 5 mid, and 2 bass. It gets woofy quick. The last parameter is the vcurve, which is a preprogrammed parametric eq like the Mark series have. The lower the number, the flatter the eq, the higher the number the more it does a V shape. Typically, you might have it between 2 to 6, more than that is overkill. It also adds gain.
The best representation of the sound is Dream Theater, though I know Metallica used them in the 90's. If you like the Mesa Mark sound, that is what it does best. It's not going to get grinding death metal, like a recto, or be quiet as full/thick, but it's an amazing unit and if you have a great tube power amp to pair it with (preferably the 90:90 that it was made specifically for) you will love it.