The TU-2 is not what I'd consider an accurate tuner.
Hit an open sixth string and tune it until the TU-2 said you've nailed down an 'E'.
Now do the same with the first string.
Now hit the 5th fret harmonic on the sixth string, followed by the open 1st string.
The two strings are not in tune!
I haven't tried the strobo, but I'd be shocked if it displayed these issues. Personally, I'm thinking of getting a tuning fork and just using my ears to stretch tune.