Yeah a DT-680 isn't going to sound good with that type of music. Same goes for almost all 3-piece boxes. They can produce great room-filling bass, but it's because they use bass ports and soft woofer surrounds, which hurts the mids. So they suck at reproducing guitar, strings, or vocals. You need stiff paper-edge speakers for that.
The only 3-piece that MIGHT sound good with that type of music is the RX-A2 / RX-6400. It's very precise and detailed sounding. The bass at low volumes is weak, but that's because it needs to be cranked up.
I've never heard the Aiwa EXOS-9, so I don't know how well it handles rock music, but it's got more low-volume bass than the RX-A2 / RX-6400. And it has more power and more modern speakers. But the advantage with the RX is that you can spread the speakers out.
As for retro old-school 1-piece boxes, the M70, M90, and RX-5350 might work well with that type of music, but people want too much money for them. The Aiwa is cheaper AND produces more bass.
The Diamondbox might be better than the Aiwa, but at that price I would rather buy two Aiwa's and spread them out for stereo effect.
If I were you, I'd buy the Aiwa, and if you like it, buy another!