When it comes to rockets, engine power is important, but so is quantity. I asked a question to that effect (Quality vs. Quantity for Rocket Engines) and got a really good answer. For a moon shot, having one super-powerful engine is all well and good, but so is having six or so smaller engines. There are the plusses and minuses of both configurations (again, see Geoffc's answer). So just because a single engine X is more powerful than another single engine Y doesn't mean that a rocket with X is better than a rocket with Y, if there are more of Y.
So if engines don't have a direct bearing, what does? Configuration of the rocket. Energia/Energiya/Энергия used strap-on boosters to supplement its main engines. The advantage of that is that, in theory, you could make modifications to add on more boosters. You also might be able to avoid the pogo problem if they were separated enough, and you have redundancy built in if the boosters are independent. Then you have Energia's second stage, which could be another smaller rocket (Polyus) or the space shuttle Buran. Polyus was really used as a one-time test, and would not have been used in later Energia launches if the system had proliferated, so there is plenty of room for modification there. In fact, there were more versions of Energia on the drawing board at the time the program ended, which were very powerful. In short: Energia would have required a lot of modifications to reach the moon, but it could certainly be modified to be more powerful with more boosters and a better upper stage configuration (a necessity to reach the moon).
The Proton family of rockets is slightly harder to analyze, partly because they are so varied, but mostly because they were originally designed as ICBMs. They use four stages to get their payloads to orbit. The first stage contains six engines (RD-275s), while the other stages use 3, 1, and 1 engines (different types). While I'm hesitant to say that Proton would be harder to modify simply because Energia's strap-ons are relatively convenient, but I will say that it would require partially (if not fully) redesigning the first stage. While the upper stages can vary, the lower stage does not.
To summarize: Energia, in its prime, would have been easier to modify than the Proton; unfortunately, it was retired decades ago. It strap-on booster design would have been convenient because in an expanded system, boosters could have been added and removed as necessary. Both systems, however, would have required extensive modification to reach the moon, and Russia overall does not appear to have that capability. I hope this helps.
By the way, some comparisons between Energia, Proton, and the American Saturn V:
First stage: E (4 boosters, 4-nozzle RD-170); P (6 RD-275); S (5 F-1)
Payload to LEO: E (220,000 lb); P (46,000 lb); S (260,000 lb)
Total launches: E (2); P (397+); S (13, with more in the extended Saturn family)