I couldn't say if there is a big difference because I have never used the time-based. I went with the Tekonsha P3 after reading tons of articles about the Prodigy and how good it was. Found the P3 online for about the same price. As my first time really doing any significant towing (BX24 on 18' tandem utility trailer), it seemed the most "idiot proof". Very easy to setup and adjust. It also supports electric and electric activated hydraulic brakes and is easily removable.

As far as brands - note that Tekonsha, Reese and Draw-Tite are all owned by Cequent. If you compare the brands closely, some models are almost identical