Here's a naysayer's point of view.
I reject the notion that certain components are good for certain genres of music. The problem is that not everyone prioritizes sound qualities in the same way. So even if you and I are listening to the same component and the same source and amp, I may be listening more for timbre and detail while you're listening for smoothness and cohesion. Ultimately we're both listening for all of those things (and a lot else), but how do we rank what's important? That comes down to individual preference.
Worse yet, I reject the notion that all tube amps sound somehow similar by virtue of the fact that they have a tube in them. However, in the case of the MG Head, it does fit the tube stereotype to some extent: rolled off in the high treble, not very fast/articulate, smooth, doesn't quite reach the deepest bass extension, a little bumped in the lower mids (lush).
You can see why some folks would prefer that for jazz. The lowest low in jazz is a simple bass drum, the band is usually only two or three members so seperation is often less critical for most listeners, an electroc guitar is often used so timbre is sometimes ranked lower, and instruments like chello and violin are infrequent in jazz, so the upper treble rolloff isn't as missed. Moreover, the mood a jazz listener gets into is often a "relaxed" state of mind and a smooth sound is sometimes far more important than articulate detail. In fact, vocals are often so important to jazz that having the liquid realism in the upper midrange often overshadows everything else.
And this is all fine. As long as you listen to jazz with those priorities, the MG Head is probably a good solution. I know people who absolutely love their MG Heads and I absolutely can't blame them. That it does so many things so right for such a small investment is amazing. It's a great little amp.
Electronica is kind of a mixed bag here. When I listen to Electronica, I do have a tendency to expect really fast and articulate sounds, but timbre has hardly any importance at all. I mean really, it's a keyboard after all, right? But the problem I face more than anything is that when I hear ambient sounds, I want them to sound realistic. If it's a metal beam smashing on a concrete floor or a babbling brook, I expect them to sound like themselves, not some electronic fabrication. Critical to this is tonal linearity. The MG Head is not that at all and combined with the probblem it has with speed, I can see why some folk would prefer some other amp with that genre.
The MG Head does have a nice soundstage/headstage, though. This might be useful to you as I sometimes (often) feel somewhat assaulted by electronica that is too forward and in-your-face sounding. Just a little distance can sometimes be a good thing. Also, that bump in the lower mids I mentioned is something a lot of people like. It makes the "beat" easier to follow and for some people more enjoyable. An electronic bass is easier to forgive inaccuracies in than it is even in drums and bass guitar, much less pipeorgans and such.
So you have pros and cons. The real unfortunate thing about the MG Head is that most people don't seem to care for it with Grado headphones. The faster sounding and a little bright on top Grados might have mated well with the MG Head if not for for impedance issues. ASL is working on a new amp that should mate better to low impedance phones.
If you're using the stock tubes with the MG Head, definitely read some of the tuberolling threads. The ability to "tune" the MG Head to your liking a bit is one you shouldn't overlook.