Never tried 6xx but wasn't a fan of HD650 compared to DT880.
No doubt they're competent, but the snowball effect of being a common first foray into hifi, the praise/purchases driven by internet popularity have probably placed them on a bit of a pedalstool.
Not liking what is most popular doesn't mean you lack an ear for hi-fi. Personally if I consider the harman curve or FR tunings/eq profiles created by popular community authorities what is popular often sound dull, stodgy and bloated to my ears.