(I have no idea.)
However, we can devise a simple research project to see which side cheats more. Just look at recounts of federal and state races.
Recounts are conducted when the race is too close to call. In the midst of a recount, many votes can be tampered with, found, manufactured, and challenged. I propose that some researcher look at the last 500 federal and state recounts of races between Democrats and Republicans. If Democrats and Republicans cheat equally, then you'd expect them to win recounts 50/50. If one party wins over 60% of the recounts, they are more likely to be the greater cheater. If one party wins over two-thirds of the recounts, they are most surely the cheating party.
There have been many famous recounts in recent memory. Minnesota just had a grueling recount of its U.S. Senate seat. And who could forget the famous 2000 presidential recount in Florida?
Unfortunately I don’t have time myself to do this exhaustive study, but it might be really interesting if a researcher took it on -- I guarantee whoever did the study would get their 15 minutes of fame.