Infiniti: it's a known reliable brand (we've owned a small flotilla of Nissans, and our sole Infiniti has 180k miles). RWD feels nice, AWD is victory in winter. It has 260/260 from the 3.5 V6, which is really nice. It's 0-60 and quarter times are actually only a little ahead of the Mazda, which is surprising. I'm not too concerned about the interior holding up with usage, the I30 with 180k feels closer to half that wear.
Only available in auto, interior isn't all that compelling, it's very boxy inside, exterior is a bit dated. Miles are quite high for being over $10k.
Mazda: it's two years newer, the insurance will be lower, it has zero miles on the clutch and motor, only half the miles on the chassis, it has a very lively road feel, very responsive, might have a small edge in MPG?.
It's a manual, which sometimes sounds fun, sometimes sounds like a pain. It feels responsive, but from throwing it into corners, I question how good the handling actually is, and how much of it is just a precise transfer of what is felt. The motor is widely considered to be weak. Any increase in motor power would void its warranty (short warranty though), and run into torque steer. I'm already listing out mods I'd want to do to the car over time.