Those are night and day guitars. I'm partial to the EBMM EVH and Axis, but they're all awesome, just a matter of taste. The last Charvel I had was a nightmare, but only because it had spent its life in Puerto Rico and took about six months to dry out when it got to Arizona. IOW, not Charvel's fault.
The Charvel is gonna have larger frets, a compound radius neck, and a nice Strat shape. The Axis is nice, but has a 10" radius, thin frets, and the bulky EVH style body.
Funny, I think Charvel necks are thinner and the Axis is more rounded but the Axis is a lot more narrow and overall feels small because of that. Ernie Balls vary though from model to model, More and Luke models are 12 radius. If anything the Petrucci might be the closest thing they make to a Charvel. Ernie Balls are made well but I find a lot of the used one's really get beat on for whatever reason.
Friend of mine has a beautiful Axis, sounds/feels killer but when I've played it I fatigue quicker. That neck profile along with Ibanez are just not for me anymore, got to have a little more to them to avoid L hand fatigue.
They're both great guitars but like others have said, you should play one to see how they feel to you. My Axis is a blast to play but feels cramped when I get higher up on the fretboard. The Charvel fretboard is wider and flatter and the carve is different. It just depends on what you like.
One other thing that pushed me to Charvels is that it's easier to get any pickup combination you want if it has a pickguard.