The train is quick, efficient, runs frequently. Advance train reservations can be a fraction of the cost of a ticket bought in the last minute. (But it's possible, you could even by the ticket onboard the train for an upcharge.)

I'd be more inclined to get the rental in FRA if (i) I had a lot of luggage, (ii) I was travelling outside peak travel times (traffic jams can be an issue otherwise), and (iii) prices and rental car agencies at FRA better suit me than the options in Stuttgart.