I have a Wolfgang Custom and I love it!
I came from 15 years of Les Paul usage, and recently found a home with the EVH brand, and now use their equipment across the board (amps, guitars, cables)
Before I picked up the Wolfgang Custom, I actually had a 76'' Les Paul Custom that I modded to be similar to a Wolfgang Custom, I installed Wolfgang pickups (bridge pickup mounted to the body), EVH pots, and even a old Gibson TP6 bridge on it... and it sounded insane...
I sold my LP custom to pick up a Wolfgang Custom.. and this is what I've noticed..
The neck to me (personal preference) is smoother, and more comfortable as mentioned, frets are smaller, and stainless steel... but the thing sings..
Obviously the body style is different, the Wolfgang pickups in the Wolfgang custom, are the same that are in the standard wolfgangs, but they are not mounted to the body, and obviously are covered... it still sounds like a Wolfgang, but it's warmer, def. not as bright as a standard wolfgang due to the woods used. I have no tuning issues with my Wolfgang Custom, and always for some reason had issues with the G string on my LP.. (on all my LP's for that matter) .. but I think end of the day it's going to be personal choice... if you prefer a Les Paul style neck, the LP is probably the choice you want... outside of the neck/frets, I think they're very similar... You could easily put the covered EVH wolfgang pickups into an LP custom, and you'd probably hit pretty damn close to the sounds of a Wolfgang Custom... but the neck, and overall feel isn't going to change, and to me, that's just personal preference... Price is even similar, the LP custom is a little more and retain value a little better... there are wolfgang customs in brand new condition floating around on ebay from $2300-2500... The EVH build quality is great though on those guitars...
I love my Wolfgang Custom, it's probably my favorite (and heaviest!) guitar I've ever owned.