I'm guessing what you have are the AKG 240Ms, since they are 600 ohms. I have both the 240Ms (600 ohms) and the HD 497s also. I became interested in my ~10-year-old 240s when someone posted about them being one of their favorite old standby headphones here... do a quick head-fi search!
The 240s sound nice, they really do, but the bass and the highs are both pretty relaxed by modern standards, but I think the tonal balance is pretty good. If you want to sit down for a relaxing, very comfrotable, long term listening session, the 240Ms might be just your thing. A legitimate and balanced but maybe outdated sound, IMHO.
If you check headroom I think you'll find some more modern 240s with the same general tonal balance but a more modern sound in the highs and lows. But for that kind of money you can get... A PAIR OF HD 580s at newegg.com !!!!
The HD 497s I think you'll notice have a lot more PUNCH in the bass and sizzle in the highs thant the 240Ms, but are still smooth. The price.. maybe the midrange is just a little de-emphasized. The 240Ms relax on the high and low ends, so that you get a comfortable, close, relaxing listen where most of the music is, in the midrange. Geez I'm full of it.
What you do have is two really different sounds.... I think that's really nice to have.