Keep in mind, you learn a lot on public. Once you go private, you are doing more repetitive tasks with little variance to the type or complexity. That makes it harder to 'move up the ladder' in private as you aren't learning much.
My impression is that those who stick it out a few more years in public are able to enter the private market at a miuch higher level as the years they've spent are highly valued.
This may all be more relevant to a corporate accounting role. less so to a local tax firm.