HD-598 has a much larger soundstage, a warmer sound and less bass.
The K240 Studio doesn't have as much treble and is close to being a dark headphone. It took me awhile to realize this.
HD-598 probably has more detail, but they're probably comparable when it comes to overall sound clarity.
K240 Studio (same as MKII mostly) would be best for those that want a little extra bass than what the HD-598 offers.
K240 Studio is also a lot harder to drive and won't work well without an amp. You may get lucky though. HD-598 also needs one despite what people say. It actually sound good unamped though. For good bass you need an amp.
Both are equally comfortable, but I guess the HD-598 has the edge.
If you do any sort of gaming or movie watching, the HD-598 is a must have.
If I had to pick a favorite, I couldn't do it. HD-598 maybe I'd take just for being open. HD-598 does have more engaging mids though.