As already stated modules aren't 1:1 copies of the amps, but are pretty close. I like to think of them as an offshoot revision. That doesn't make them better or worse from their counterpart; just different.
One thing that can't be stated enough is the influence of the power amp you're using.
For examples:
My Powerball and Savage modules sound and maybe more importantly feel more like
Engl's when I run them through either my ENGL Morse or Inferno.
Running my IICP module through my Mark III Red stripe's power amp, they're almost indistinguishable. I would lose track of which one I was on when switching back and forth they're that close.
In contrast if I put any of those modules in my Randall RM100 they would sound & feel slightly different. Not a huge amount, but enough where I could hear the difference between the Mark III and IICP in the Randall.
Power amp selection will be dependent on your setup and what you're trying to accomplish. If you're going to be using a number of different modules a Fryette powerstation may be your best bet. It's fairly transparent and will work well with most everything across the board. The downside is you don't necessarily get the feel of big iron with it. If you're going for a specific sound/module you are likely best to choose a power amp that's similar to the real thing. It may not work as well with other modules, but will hit the sound you're going for better. The main thing here is to start with a good power amp and you'll get a good sound. If you go into a crap power amp it'll end up sounding like shit.
In my case I started out with a Fryette PS100 which worked just fine. I've recently changed my setup where I'm using a couple of Synergy modules and some modded MTS ones for both bass and guitar. So I've migrated everything to my Crate BV300. This is the one from when Crate and Ampeg were both owned by St. Louis Music. The BV300 has a SVT power section. The SVT power section gives me the best balance for everything. Not to mention 300 watts of huge iron hits like a truck when you start to crank it.