I don't want to get too in depth or wordy, so I'll just break it down into some headphones I think you should check out:
Sennheiser - HD650 and HD600. The HD800 are good, but they seem to be love/hate, and with their price, and the fact that they don't particularly excel at the two genres you listed, I don't think they'd be a good fit.
Denon - D2000/5000/7000. All are similar and more or less based on the same design. Have been compared to the HD650 sound wise but also have their own unique sound. I've heard the D2000 and its very good. My recommendation would be one of the Denon models. You could try the D2000 for fairly cheap, and if you like them a lot you could sell them and move up to the D7000s
Audio-Technica - W1000X, AD2000, maybe the A1000X/A2000X (not a lot of feedback on the latter two, the W1000X is fairly new but already pretty well liked, and the AD2000 should be good for the two genres you listed). I'm a big W5000 fan myself, but they have a lot of quirks, and unless modded aren't great sounding for the two genres you listed (they're like the HD800).
AKG - I don't know that they have any that fit really well for what you're looking for either, and many of their better headphones are in production. I thought they were supposed to have a new flagship this year, but I think its gotten pushed to next year.
Beyerdynamic - DT770/880/990. All 3 are roughly HD650 level. They also have the T1 and I believe should have another high end (like the HD800, means $1400) headphone very soon (based on the T1).
Ultrasone - a bit more polarizing (love/hate responses) than other brands. HFI-780 and Pro-900 for midrange (well I think the 900 is more upper midrange, like $400-500 range). Also have the Edition 8 in the high end, and will have an Edition 10 very soon (even higher high end, possibly $2000-3000 range).
JVC - Victor 700 and 1000 I think are the models. No personal experience and not a ton of people that have them, but most who do like them quite a bit.
Stax - no particular models, but you probably want to go higher end to get the best. That or vintage. Also keep in mind that they're electrostatic so they'll need energizer (special amp).
There's a ton of others I know I'm forgetting (there's a couple of new headphones that are popular and would be more comparable to Stax, one is I think Audeze LCD-2, and the other is Head-Direct EF-5?), but this will be a good starting point.
Oh, on the portable end, I'd say check out Audio-Technicas mid/upper-mid ESW9, ESW10, and ES10. There's so many IEMs to go into that I can't even begin to cover it (and feedback is all over the place). I will single out the Westone ES3X and Jerry Harvey Audio customs.