I am by no means an expert on this topic, but I do listen to a lot of metal and hard rock, of many genres.
My take on it has two sides, technology and tuning.
I was reading this thread earlier wondering if someone would ask "what is modern metal tone". I started listening to stuff so that I could show examples of "this is X type of Metal tone". Except, I noticed a trend.
Tuning - Almost every band that I would classify as using a modern metal tone drop tune. You have everything from standard Drop D to guys downtuning to C and then all the 7 string players with B or Bb. These drop tunings roll a lot heavier and thicker, but yet they all come across clearly, much more so then in previous eras.
Technology - While looking at some stuff I listened to a bunch of remastered albums (mostly Megadeth). When you A/B a lot of remastered metal you find that a lot of the "classic" metal tones are much heavier and aggressive, more modern sounding when remastered. The technology at the time didn't necessarily allow for the low end to be as present, the highs to potentially be overly present, and sometimes the mids were mixed up to compensate for the lack of bass. As well modern tech has allowed much cleaner applications for gain saturation.
So, ok, I am making a bit of a generalization here but those combined point to the fact that as technology has improved, denser music, with a lot more low end has been more accessible.
So perhaps that is your answer to "What is Modern v Classic Metal". It is that modern technology allows for much cleaner application of high gain, punchier more present bass and cleaner voicing of individual notes even on the lowest tunings.
Now, which bands apply this...that is personal preference I guess. I point however, to Rob Halford. If you listen to early Judas Priest, it had a "classic" metal tone, but if you can, listen to Halford - Live Insurrection (where he plays several classic Priest tunes). Yes it had a lot of post production but, the tone is a lot of heavier without sounding terrible.
With all of that said though, whether it be modern or classic, the tone you want should be what you own. If the Mark V gives you the tone you want, then great. If not, there are dozens of other amps you can buy.
You guys, writing all that while I was trying to post...