I've taken, both, generic levothyroxine (T4) and liothyronine (T3), as well, as brand name Synthroid and Cytomel. I did better on on generic levo than I did on Synthyroid...
I've been taking generic liothyronine for over 5 yrs and have done just as well as I did on Cytomel.
I don't think you'll have any difficulty, with generic T3, but if you do, you can always go back to Cytomel.