No, the biggest thing that will throw you is the change in mouthpieces. The size will jump, and so you will have to get used to the large opening. No, playing in the right key is pretty easy on both horns.
It's just the notes that bother me. How do you finger a B again?
Adderley - If the music is already transposed for either alto or tenor sax, then it obviously won't be a problem as long as you use the right sax with the right music.
Tenor will be marginally easier as there'll be one less sharp in the key signature, but if you have to sight-transpose from keyboard/vocal music then you'll have a quick learning curve - as you'll have to read one tone up for the tenor, then switch to a minor third down for the alto (or pretend you're reading bass clef, with a few adjustments).
If you play 'by ear' and have good perfect or relative pitch, again your ears will have to re-synch with your hands. neither of those are insurmountable.
I spent years switching between flute in C, sop/ten/clari in Bb, and alto in Eb. The hardest thing I found was developing an individual style on each, so (e.g.) it didn't sound like tenor phrasing on alto. Not such a problem if just reading band parts.
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