Yes, but where is Putin limiting presidential power? He had no need to do so because he controlled Medvedev.
Well, some people say that under Medvedev Russia was a bit friendlier with USA:
https://en.wikipedia.org/wiki/Russian_reset
I'm not sure that points highlighted in that article would happen if Putin was president (allowing U.S. forces fly over Russia, supporting Iran sanctions, reducing nuclear arsenals, U.S. dropping plan to build a missile defence shield in Eastern Europe).
The other stuff - seems just like Putin thought "well let them think Russia has changed".