I've owned 5 Wolfgangs. 2 Standards, 2 specials, and a Flametop Special. The last one I owned was the Flametop Special, which for all practical purposes is basically as close to an Axis/EBMMEVH as you can get and still call it a Wolfgang. After I got over the novelty of having a guitar with EVHs name on it, I tried an Axis. I have owned 3 Axis' since then, and haven't looked back since.
I can't knock the Wolfgang. It is an outstanding guitar. It is just not up to the quality of the Axis.
I wouldn't say that you are missing anything by not having one. There are some differences that you may appreciate though. The fretboard on the Wolfgang feels quite a bit different than the Axis/EVH. Going from the EBMM to the Wolfgang kind of feels like going from a Strat neck to a Les Paul neck. Fretboard seems flatter, to me anyway. The pickups on the Wolfgang are quite a bit different as well. They are a little darker, and don't clean up as well. The Wolfgang would be better for plugging into a Dual Rectifier than a EBMM would.
I kind of liked the carved top on the Wolfgang too. It made the Wolf a little more comfortable to play than the EBMM.
If I were you, and I had the money to spend, I would recommend picking up a Wolfgang Standard Stop Tail. You already have an EVH guitar with a trem, so why not have one without. The fact of the matter is that the Stop Tail Wolfgangs sound better than any of the other Wolfgangs out there. Maybe it's the combination of the regular nut and the stop tail, or maybe it's because there's more wood due to the lack of a route for the trem springs, but the thing just sounds great.