I used the Ultra's tuner on the front panel for 1,5 years. After that I replaced the Behringer footcontroller with the Gordius LG2 and have it displaying the tuner info from Ultra/II ever since. Works great!
I have only had my Axe for a couple of weeks and the tuner seems allright. I have not used the Axe live yet and with my previous rig (pod xt, etc..) I used a Peterson Strobostomp which I am very satisfied with.
Do you use the tuner on the Axe live?
I will keep my strobostomp anyway for tuning in the studio and intonation.
It is a little disconcerting that the tuner on my Ultra (which displays perfectly on my Liquid Foot LF12+) disagrees quite a bit with my two Snark tuners (which EXACTLY agree with each other). I have yet to really sit down to decide which tuning sounds more right to me. but anecdotally, I think it's the Snarks. I would compare it to several other tuners (snarks are like $10.00 and great to use) before you decide to rely on it.