2 professors from the same university same department have agreed to be my mentor. But none have funds, prof.1 may give me TA, while prof.2 can give me RA. Which one should I choose? Can I put 2 applications with 2 different SOPs and then decide later which prof. to go for?
I would counsel against two different SoP statements. If they are compared then it makes you look like you don't really know what you want. The university might be fine with two separate applications (or not).
But more important than the source of funding and the activities to earn the funds is the question of what would the research be with each of these people and can one of them better support your career. Make your decision on that basis.
Bot the TA and the RA experience can be valuable for an future academic, but in different ways. But that is less important than the research opportunities.
I'll guess that the TA position is probably easier to manage your time than the RA position, but that isn't necessarily true, depending on the nature of the university and of the field and department.
You might consider trying to set up a three way conversation to see if the two profs have some advice for you about which would be more suitable and advantageous. But that assumes that you know something about them first and are sure that it won't generate bad feelings.