How much of an advantage does 30 some more charge give?
If you watched the video in the OP, virtually nothing compared to an insanely high defense. The one time the cats got a decent kill off of their charge, it didn't take too long for the other cav unit to even the odds and then gain the upper hand.

I just started trying out the Socii Equites Extraordinarii you can recruit with a high level auxiliary barracks in Italia.
The Romans with heavy cavalry?... in this time period?? that's just....well it's just not right (first recorded use of equites cataphractarii was around the 2d century AD although 'armored riders' were 'in use' as early as the 2d century BC). Definitely a nod to the "console crowd"

They hit VERY hard, but if they don't rout what they impact, they're going to be in trouble without support.
This. If you look at how the Parthians used their cats, they almost always had CA support nearby after the debacles at Magnesia (189 BC a Seleucid defeat) and Tigranocerta (69 BC an Armenian defeat), Carrhae (53 BC) being the perfect example.

In my Armenian campaigns for R1, my heavy cats worked best when echelon-ed...the first wave hit and disorganized formations, the second delivered the killing/routing blow. I did a similar thing with Seleucid cats, only the first wave was scythed chariots. The support came from CA's out on the flanks who would switch from archery to melee shortly after the heavy cats hit. Now R1 is certainly no shining example as a battle sim, but heavy cats did seem to work better with support.