I have used the Arduino Mega at home for hobby stuff, and having used the TI C2000 real-time processors at work, I believe the TI processors (like the TMS320F2803x) have much better specs than the Atmega2560. They are 32 bit, are, faster, and their peripherals, such as PWM and capture timers, are more advanced.
Unfortunately, there is not a huge open source community built around the TI stuff. While the TI examples, and code composer studio are nice, choosing a TI processor still means you have to write a lot of new code for sensors and timers and things, and you can't necessarily find blogs for people doing similar tasks for guidance.
At home, I still would much rather use the Arduino Mega for my robots because there is SO MUCH code already written. It's hard to find a sensor or microchip that DOESN'T have an easy to use Arduino library. The Arduino forums are likewise-amazing in that there isn't a question I have had that isn't already answered 10 times over. Sometimes I am a little frustrated by some of the limitations in the Atmega hardware, but I can usually make it get the job done.
It would be nice to see a TI C2000 arduino board, similar to the mega, that could combine the best of both worlds.