The one-on-one says it all, though. EI also did better against all other units tested: Barb. Cav, Swordsmen, Scythe Chariots, Archers, Militia Hoplites. So yes, EI are better.
I never did any empirical testing like the folks at TWH, but my battlefield experiences told me that EI were better against most other units than Hillmen, and, as you pointed out, they are cheaper to keep.

I just don't like giving up cities so I keep Sakae.
Can't fault you there. However.....in one of my early Parthian campaigns, I ended up at war with Scythia, Seleucia, Armenia, AND the Big E. Not much fun when you run out of money because you have to keep so many armies in the field to fend them off. So I greatly reduce the possibility of war with Scythia by removing their closest target. Even if they send an army south to attack you in Colchis or Media, crush it and they will be hard pressed to send another for a very long time.

and a Scythian general with a horse archer army moved in and out of Sakae several times
........what I said......

When I move capitals it will no doubt give me trouble but that is expected.
Once I take Seleucia, Hatra, and Sinope, my capital goes to Hatra, so I just anticipate the inevitable.....you don't have a good enough law-and-order temple to swing it, and getting it to ZPG is verrrry difficult.

RS may have something to say about that
Your a horse archer faction here, not a bunch of stone-chuckers