It depends on how you want to define it. Are you only looking for presidential scandals, or all scandals involving politicians at the federal level, or just all big-name political figures? Also, what time frame? The worst presidential administrations were all Republicans, but before Bush, Nixon and Reagan the party affiliations weren't as meaningful. Warren G Harding was a Republican, for instance, but the parties were different then. I don't agree that the Republicans were the liberals back then (Harding was reportedly a member of the KKK, as was Wilson, a Democrat), but the issues were different.
When you get down to the state and local offices, it usually depends on who is in power. Power draws corruption, so the part that has a lock on elections is going to draw the most corrupt people. In Texas during the fifties there were a lot of corrupt Democrats, and the Repubs were probably more pure, since only true believers would have bothered being Republican. Now that's reversed.
I don't frankly see how it matters which party has had the most convictions, so much as which ideology has the best record of results. Liberals (not necessarily Democrats) were against segregation, apartheid, slavery, McCarthyism, the Viet Nam and Iraqi invasions, tax cuts targeted only at the wealthiest, etc. Conservatives (sometimes Democrats) were for those things, and against women's suffrage. Liberals were trying to fight Fascism while conservatives like Henry Ford, Father Coughlin (30s version of Rush Limbaugh/Jerry Falwell), Prescott Bush and Charles Lindbergh were actively supporting them. Liberals are more often right, and whichever party is the most liberal most often advances the causes of humanity, while conservatives hold it back.
But as for corrupt presidencies, the Republicans, especially in the current era, take the cake. And that's despite the fact that the Republicans spend more time trying to smear their opponents, since they can't win on the issues.
http://liberalslikechrist.org/about/Reagan.html"By the end of his term, 138 Reagan administration officials had been convicted, had been indicted, or had been the subject of official investigations for official misconduct and/or criminal violations. In terms of number of officials involved, the record of his administration was the worst ever."
LONG list follows (see link)