I think they're a bit different, and "small business tyrant" is in some ways an improvement. Every small business owner is petite bourgeoisie, but not all small business owners act as tyrants. There are some (I've worked for them) whose businesses are scraping by, who are extracting little if any surplus value from workers, and who are generally treating their workers decently. Lumping these people in with a multimillionaire car dealer who exploits the hell out of workers is theoretically imprecise, in the same way calling everyone from a petty theif to a mass murderer "criminal" is.

Rhetorically, it also targets the criticism at the multimillionaire car dealer rather than the small baker with two employees. "Small business tyrant" does a better job of focusing the conversation where exploitation is most clear.