The Anandas seem like another alternative to the Edition XS, but for a nontrivial additional $200, and I am not sure how different they sound from the XS and in what specific ways.

I haven't had the XS since they were first released late last year but from memory, you will definitely get more "slam" and bass extension than HD650. The mids on XS are scooped and it would an adjustment coming from HD650. Not necessarily a bad thing...just different. Hifiman cans tend to have a dip in the 2K region but it was quite noticeable on the XS. Nothing a bit of EQ can't fix. The mids are definitely better on HD650s. Treble is as you described...much more forward and detail retrieval is much better on XS. The one thing I will say is that the soundstage is much wider and open on the egg-shaped Hifiman. That will be something you will definitely notice vs. HD650. At the end of the day, yes, they are different enough to serve as a good compliment to your 650s. I just don't think the XS compared to the HE-500 so I ended up selling them.

I will say this though...I did the Custom Cans mod on the HD650 and it made some pretty significant improvements to the stock sound. So much so that I've sold the XS but still have the HD650 so it says something about how much of a staple the 650s are in any collection.

I have the 6xxs and Edition xs. The edition has more clarity and soundstage, but the 6xxs are more intimate and warmer. They both sound great imo

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I have the 6XX’s( not the 650’s ) and the Edition XS’s and yes 2 completely different headphones. The big problem I have with a comparison is their difference in amplification requirements. I for one believe if you have not heard a 650/6XX from a Bottlehead Crack you have really not heard them. I have several amps but for me only a few that I think are good with the 6XX’s .
First is the Drop Cavalli Tube Hybrid. It is not a matter of power just that it meshes with it more than say a Magni or Atom.
The Next is a iFi Zen Can Signature 6XX just Awesome the iFi team hit it out of the park with this amp. The EQ and XSpace are done so nicely without being overbearing.
The Bottlehead Crack is the best I’ve heard the 650/6XX’s without a doubt. Some of the best mids ever. I do have a affinity for a Tung Sol 5998 as the power tube.