There’s a difference in the ability to make it happen across the board. There are already places where there is no exception to minimum wage for service workers, but there are many places where it would be extremely difficult to make happen. Whereas changing the tax on tips rule would face much less political blowback.
So yes, it’s much easier to make the tax change than to make the federal minimum wage both a living wage and apply to service workers. Pretending that political feasibility doesn’t matter in how quickly it can be accomplished isn’t helpful.