According to the best information collected in the below article, SR and MMR match, since they move at the same time. The only exception is for Leaver / DC penalties, and Decay. It may even be possible that MMR no longer exists in Competitive.
All according to this article:
The MMR formula for Competitive is transparent. They’ve said it moves exactly as much as SR, and hinted that it actually no longer exists.
I don’t think this is true. According to the article, (which is a well researched collection of all the information that has been made public, including links to the source materials) they try to match solely on similar SR for all 12 players. There’s also the “find a match quicker” mechanism which does accept larger gaps, but there is no evidence that this is in response to someone’s recent performance.