I have a Bogner XTC 101B and a few of the EVH amps and I can say they are much more similar than you'd think. The EVH has more built-in cut in the lows at the input so its distortion is going to be more articulate out of the box, but if you add your own low cut to the XTC at the input with a pedal, the amps can be made to sound strikingly similar.
However I will say that EVH amps can easily get big and wide sounding too if you crank the Depth and Bass, and pull back on the High and Presence knobs. The EQ controls on the EVH and the Bogner are all after distortion, so they don't change the character of the gain. Instead they operate more like how the EQ on a stereo works.
The Bogner can give you the option of squishier, more vintage tones because it has less low end filtering at the input, whereas you can't really add back low end at the input in the EVH because it is internally filtered away just after that in the amp, but if you're going for a big wide high gain sound that is still articulate, you really can't go wrong with either. They will both do exactly what you want I think.
Once you add a pedal that cuts lows and maybe boosts everything else to the XTC, I don't know how else to say it but the differences are broadly that the EVH feels slightly harder and more modern by like 5-10%, and the XTC has just a bit more "bounce" to it. I hope that translates but seriously the difference is small.
edit: I found some old clips to clarify what I'm talking about. This is a guitar track that was recorded direct and reamped through both heads. One clips is of an EVH 5150 III 100w EL34 and the other is a boosted and low cut Bogner XTC 101B. I believe the boosting and cutting on the XTC was done with a Boss GE-7. Both heads are running through the exact same signal chain, same reactive load, same IR's, same everything. Also no knobs were dimed so any slight differences in EQ could probably be accounted for fairly quickly and easily. If the EVH doesn't sound quite as hot as the XTC, a boost of just a few db's at the input or maybe just turning up the gain knob slightly would probably negate the difference, etc.