it's a compromise.
If the HD 800 is 70% compatible with your music collection then the HD800S is at 90 (modded 650=100%). That's quite a huge step, especially on more modern and synthetic stuff.
HD 800S sounds sharper and can be a bit more exciting. The very nature of certain peaks. It's why many Beyers are released on the market with them as many people love the excitement they bring, even when it can lead to fake detail. You know that though.
The HD800 peaks works similar. It's less offensive than a T90 or DT990 but it's there. It can have razor qualities, a certain sharpness and liveliness. It doesn't really matter much with classic but it's infamous with quite a few people's favorite tracks and genres as it messes up with many modern recordings with most gear. Something like Odac/o2 should be avoided.
HD800S
-lower bass extension
-fuller bass, hits harder
-more physical/tactile
-peak pretty well tamed
-sounds more natural in Klangfarben (the very way an instrument or object sounds, its character, should be timbre in English)
-still the same huge and cohorent soundstage as the HD800, imo more cohorent as the resonance in the cups is mostly gone.
-slightly less separation or not quite the reference separation of the HD800 but that's quite a luxury "disadvantage"
HD 800:
-sharper, more razorlike effect in separating detail/instruments, it's subtle but it's noticable
-6K peak leads to less natural Klangfarben but shouldn't matter to most people anyway as few hear instruments regularly or daily
-due to tonality the sense of air is a bit bigger
-lesser bass extension but still that ultrahard and ultratight kickbass, can still go into subbass regions
so in the end: get the HD800S and have more benefits for better music compatibility, tonality, overall better package.
get a used HD800, mod it french style and love it for its few specialties/advantages.
for gaming a HD800 is already overkill but man, that Philips Dolby Headphone device I recently bought and a HD800. A TH-900 goes lower and is supreme down there but a HD800 soundstage and sense of space remains unique