While there is no official scorecard, various tallies suggest that in the past 50 years criminal indictments and convictions of executive-branch officials and have been much higher during Republican administrations.
A fact check by PolitiFact in early 2020 recorded 142 indictments—formal criminal accusations—related to three recent Republican administrations (Nixon, Reagan, Trump) versus two indictments during three recent Democratic administrations (Carter, Clinton, Obama). Since then, more Trump associates have been indicted, including Steve Bannon and Tom Barrack.
In 2018, the Daily Kos, using Wikipedia's list of federal political scandals, enumerated 88 court convictions—a formal declaration that someone is guilty of a crime—during the five Republican administrations since 1970. In comparison, the three Democratic administrations since 1970 were associated with two convictions, both during the Clinton presidency.
Fifty-five of the 88 convictions occurred during Nixon’s presidency, followed by 16 under Reagan, nine under George W. Bush, seven under Trump, and one each under Ford and George H. W. Bush.