2. Math, short of a PhD, needs, for job purposes, something else to apply to. Computers, physics, economics, teaching, etc. Physics not so much - with a masters in physics, you can work as a lab tech.
3. With math, you're learning sophisticated trivialities. It's all just a game: some human makes up some definitions and rules, and then mathematicans go and find the necessary consequences. Physics is about REALITY. Physics isn't a matter of logical necessity, but an exploration and discovery of the contigencies of our actual reality. Since logic is non-ampliative, math ultimately gives you no *actually* new knowledge. The only true epistemic meat to be had comes from science. So in that sense, math is a game, physics is serious.