Amen!I am sort of leaning in the same direction.
I don't love the Axe tuner, and it has nothing to do with precision, but it has everything to do with ballistics. With the Axe tuner (especially displayed on the FC), I feel like I move the tuning peg and wait for the tuner to stabilize. With the Peterson (that I just got today), there is a real time connection between moving the tuning peg and the movement of the tuner. It feels more trustworthy, and it makes it faster to tune up.
It will not be easy to integrate a strobostomp in my setup, but I am thinking about bringing the Stroboclip (got both) to gigs and just use the Axe for tuning maintenance.
I find the Peterson to "settle" on the tuning string super fast - way faster than any chromatic tuner I've ever used. And it's insanely precise - within 1/1000 of a semitone (fret). The Korg "Cylon" unit, and most stomp pedal tuners I've seen, were radically less precise.