I've owned three T50C's and a reissue Model T. Aside from the reverb and power difference, yes, they're essentially the same amp. Of course, if you only run the T50C with its internal speaker, it will sound quite different from the Model T being played through a closed-back cab.
Thankfully, the T50C allows you to simply unplug the internal speaker and connect as many external cabs as you'd like, at least down to a 4 ohm load.
I enjoyed both amps, but I prefered the T50C because it can be switched down to 12.5 watts, which really allows you to crank the amp and get great, natural distortion. Even at 12.5 watts, it's ungodly loud. At the full 50 watts, it's loud enough for any gig.
The Model T reissue can be switched down to 25 watts from 100 watts as well. With the matching 4x12 cab, it's truly a phenomenal sound, but it's more power than many people need.
Neither amp has anything in common with the original Model T's, but both are fine amps in their own right. It really just depends on which one better suits your needs.