The shoutyness difference is insignificant. Hekse have a bit more energy at 3khz, Arya Stealth have more energy at 4khz.
Hekse's 3khz a bit higher than it should but it doesn't really bother due to staging/detail capabilities of the headphone and the distance it creates. Ananda was a big offender to me in terms of shout.
It's hard to describe. Hekse's stage isn't massive and it can still get intimate. I think all egg shape Hifiman's can do that. However it's not as intimate as Arya Stealth. Music doesn't really feel distant but mids feel a bit distant relatively. It's still an engaging and intimate headphone when it needs to. If you read comparisons between old Hekv2's and Hekse you will see that Hekv2 users complain Hekse is ''too energetic and forward''. So it's kind of a middle ground i guess.
I read a lot about Hekv2 Stealth too. People actually praise it's bass a lot so if you like bass i'd say go for HEK Stealth. Hekse doesn't really excel in bass. It does the bass perfectly but nothing beyond. Where Hekse excel is separation and spread out imaging. Excellent detail. It's significantly better for gaming and movies in my experience. Arya Stealth's had a bit more bass oomph but it's imaging was lackluster in comparison.
I strongly recommend this guy's comparison: https://www.youtube.com/watch?v=L2zibq8UIho