Not really an audiophile here so I may not be explaining things well. Owning both the HD650s and HD598 running off a ODAC/O2, I find the HD650 to be incremental but significant step up. I prefer the darker sound signature and tonality of the HD650 by far. It's more detailed, feels like a more natural vocals (tonality?), more laid back, and has better imaging despite the smaller soundstage. To my ears its clearly the better headphone.
Preferred it by far to the K7XX by far as well, which seemed colored and artificial in the mid range in comparison.
The HD598s have a bigger soundstage, but less accurate to my ears. Not sure about the E10k though, someone else can probably tell you if that is a sufficient dac/amp & pairing.