Posted on July 29, 2013 at 02:25TC infers the last bit hit the wire, which presumably would be a stop bit or two. TXE on the other hand indicates that the holding register (not the shifting register) is empty, you'll likely see this around the time the first bit of the previous content of the holding register hits the wire.
Waiting on TC being the least efficient way to utilize the serial port, and potentially having larger inter-symbol gaps.
