Is it mostly a problem of the 1700 AD scenario?
I have a feeling that it is, though it could also be a difference in expectations. If I run a 600 AD America start I expect there to be a civilization or two that has a score at about 1500, England ahead of me by 3 or 4 techs.
I think a big part of the problem is that infantry come too early, in fact most all of the industrial era units do. Pushing these units back and having more national wonders/projects/building could help. Maybe something having to do with imperialism that is spaceship-like (multiple parts so gives all cities something to do)?
Edit: Russia seems to be too powerful in general nowadays.
I think more units, less buildings would be appropriate, although it seems like whenever an adjustment is made to them they either get really powerful or sit in the dumps. In my case, I often see them behind, except for an occasional game when they are about average. Note that I play almost exclusively 600 AD scenario.
It feels like they would be a lot more predictable if they were to spawn post-Mongol. This is why to me, a Russia split (pre-Mongol Kiev, post-Mongol Moscow) has always been the best case for a new civilization, but I doubt you are too in to doing that.
While on the subject of the Mongols, I think their old UP (Keshiks upon city conquest) was much better for the AI than the current one. Maybe this could be an AI-only effect or something that could be added to their current UP. Might also be that the stacks are not big enough, but much bigger would be awful for the human defender.