The comparison to a specific amp is relevant to a player who knows that tone. Normally that means someone who has played the amp, but it could also apply to someone chasing a recorded tone where the gear used is known. In either case, you’ll know because you know what sound to expect. In those two instances, yes, it matters.
Otherwise, there are so many great sounding amps available, your options are to sample them until you find what you like, or sample until you discover something you love that you didn’t know existed.
I feel bad for people who get hung up on the hype, the net gossip, and forum lore about what is and what isn’t. Screw all that. Use you ears, pick your poison, and make some music. Honestly, if you can’t find a suitable tone in the Axe Fx III, it isn’t the gear. Go have some fun.