Carvin cabs are definitely solid. But every time I have used a Legacy cab it has been with a head that was crappy and I wasn't familiar with. Specs look good though. Carvin uses Vintage 30's which are great. They also use Poplar plywood.
What is in your Avatar cab? They use heavy duty baltic birch and the 2x12's have a good amount of internal volume. Solid jointing and seals. What speaker is in there? Is it Open or Closed back? Mine is open back with a Vintage 30 and G12H30, and it has a TON of low-end. Sometimes too much for live use, especially up against a wall.
With speakers it is all about internal air volume, and a good balance. With guitar cabs, resonance of the wood is typically desirable. But many consider MDF (tonally dead) to be better for styles like metal. Even high end manufacturers will do MDF in their cabs. The biggest downside to MDF is it more susceptible to water damage, it is heavier, and it can crumble at the edges.
Universally, it is pretty much accepted that good speakers is key, and they make a huge difference since they color the tone so much. Also the baffle must be well braced. Then in sealed back cabinets like 4x12's, that back better be sealed. I mean some guys like the leaky Marshall cabs, but almost everyone that has sealed it up liked it much more.
So on the cheap, find a cab with similar dimensions and then get good speakers in it. So Carvin should be a solid contender. Avatar I think are excellent cabs. But for 4x12's from them, get the Contemporary or Vintage which are 14" deep vs. their standard that are 11 or something.
I like Vintage 30's a lot, but they are mid-spikey and lack some low end compared to many speakers. An SM57 lacks lowend and has a midrange honk too, that just works well in the right spot. I roll off really high in the mix anyway to make room for the bass.
Under a mic you have so many options. For more lowend put the mic closer for proximity, move it more towards the cone, put the cab on the floor, or closer to a back wall, or even a corner for super boomy.
But what head, what mic, placement, speaker, open/closed back, etc? You might just be having a problem with the speaker choice, or that sound in general. I mean for as many lovers of SM57's, you can find just as many haters or people with a preference to i5's, 421's, SM7's, Royer 121's, Fatheads, e609's, e906's, U87's, 414's etc. on guitar cabs.