hey101:
He decided to use STP16 chips and software to handle the pwm instead of going with the TLC5940. Would that be a better option or which would allow for smoother transitions in the animations?
I don't think it's a good idea.
Problem: Where are you going to store all the RGB data for the sequences? It's a huge amount - 3k per frame. Even an Arduino Mega or Due won't store more than a few seconds of data, you need something that can store gigabytes.
If you use something like an SD card to store it then you'd have to update the PWM and read the SD card in parallel. Not going to work out well...
The TLC5940 takes the load off the CPU so you should have plenty of time to prepare data for the next PWM cycle.
nb. The guy in that video seems to have his cube connected to his PC