I'm going to respond again here rather than starting my own thread about this.
I threw on the free set of 10s that I got a couple nights ago. The truss rod maybe needed a teeny tweak. Nut was totally fine, but I had previously filed my nut with the Stewmac gauged files, and this may have resulted in my slots being a teeny bit wider than a stock fender nut.
I found bizarrely that my saddles needed to be tweaked a teeny bit to keep everything the same height at the 12th fret as with the 9s. Intonation didn't really change at all and I didn't see any difference in whether I was fretting things sharp or flat, vibrato wasn't any harder. The truss rod needed a little tweak but that didn't seem to have a big effect on feel.
I took the 10s off this morning. For whatever reason I just didn't like the feel, and the sound wasn't doing anything for me either. Lots of people here seem to imply the bigger strings have more tone or hit the amp harder or something. For me they seemed more balanced maybe, but it seemed like there was actually less output if you played at the same intensity. Cleaner sound cause you seem to need to hit the strings harder due to more tension? Definitely less "twang" and "bark", it feels like the 9s have more character. The positives for me are it seems like the 10s make it easier to keep the bass strings under control, while also taming the treble a little. The higher tension/mass seems to keep the low E from ringing out as much from sympathetic resonance, and if you don't properly mute the bass strings it seems like you can get away with it a little more. Also I think open/cowboy chords sound a little better with the 10s on my guitar. More note separation and clarity particularly for clean sounds. Hammer on/Pull off and Trills maybe suffer a little on the 10s. Also the 10s seemed more resistant to rattles and such that you would hear when the amp is not turned up loud, but those don't really affect your sound anyway.
No trouble bending or anything but I was finding barre stuff annoying. Not just 6-string barres but also the little mini barres you do when playing triads. (I'm doing a lot of this right now for lessons). It was just enough to be annoying and cause my arm to be a little tired at the end of an hour of playing.
I'm kind of wondering if my guitar just really wants to be on 9s. The feel on the Tele with 10s is seemingly harder than my acoustic with 12s, and the total tension on the acoustic is considerably higher. (IIRC the Tele with 9s is 84lbs, Tele with 10s is around 102lbs, and the Acoustic with 12s is 152lbs.) Who knows what the heck is going on. My Acoustic is a 24 7/8" scale Taylor with a 1 11/16" nut (same as Tele) and the neck and fretboard don't feel that different but acoustic has a flatter fingerboard radius. (15" I believe). The Acoustic with 12s is not as hard/finicky to barre as the Tele seems to be with 12s.
Who knows, maybe I'll try them again in another year but I think I just like 9s. But maybe it's also that I just don't want to take the time to adjust. The other thing I guess is I mostly play D'addario strings. Neither set of 10s that I've tried were D'addarios. Maybe there is something in that, but the gauges were the same.