The obvious financial choice is the Corolla. But there are a couple of unique factors that might push the decision the other way. First is your back: if you have damage to your back that is going to create chronic pain, I would not take a chance on a seat that I *might* be able to make comfortable if I change things around. I have been struggling with much more minor back issues for the past year or two, and it is ridiculous how much the chronic issues interfere with my ability to be active and lead the kind of life I want. So keeping my back functional and healthy has honestly become my top priority, because it is such a necessary component to enjoying the rest of my life.
Second is the safety: I have been persuaded by the active crash avoidance features, and our next car will have them, period (though I hope that will be several more years so used cars with those options will be more available and cheaper). It sounds like the Mazda has at least some of those features -- does it have the whole package? (I care less about the backup stuff than about the active braking) And Toyota also offers a similar option; does the one you're looking at have that package?
And then the other aspect of safety is your own feel driving the car. Which car do you feel more in control of driving? Personally, I have never found a Toyota I felt comfortable driving, because the handling was sloppy and loose; I much prefer the tightness of the Mazdas.
So if it were me, I would buy the Mazda, assuming that it has active crash avoidance and the Toyota does not, because the extra money would be worth it for me for the comfort and safety and "feel" of control while driving.* But it's really up to how much you value those features. And on the flip side, look at the total cost to own, too -- the 6 is a much larger car than the Corolla and will likely suck more gas and may cost more to insure. And I don't know the particular repair history of these models.
*I also say this only because you have no debt and a good 'stache. You are at a point where you can afford some "extras" beyond the most basic needs; you just need to decide whether these particular extras are the most important ones to you, and if they are worth the extra time you will need to work to pay for them.