(To be clear, Bloomberg can do what he wants, but I'm sick of the Democrats acting like they're the "money out of politics" party when they routinely outspend their opponents and take donations from public-sector unions.)
The difference is that Democrats will still criticize Bloomberg all the time and nobody's going to change their position on an issue because of his spending. Republicans, meanwhile, are terrified of the NRA and essentially delegate their entire policy on guns to the organization and have to constantly kiss its ass and defend the indefensible.