As far as I can tell the only difference is that the Replica is true-bypass, and the TC isn't.
I stand corrected here(!).
I went to submit a question to the TC Electronic support guys to ask whether the Vintage Delay is true-bypass, and it had already been asked before. It appears that the pedal IS true-bypass, although why they don't list that as a feature of the pedal I can't explain!
Cheers,
Jordan.
ps. Given that info, it would appear the pedal is identical to the T-Rex Replica.