I train my right side much harder then my left. The reason I train with my left at all is so that I'm not a complete dunce if I have to put a weapon in that hand. Lately, I've been trying to take unig zyow and turn it into a left hand form. THAT is hard.
Once your body learns how to move, it doesn't matter much which side it moves with. Sure one side might be a bit more precise, but when you truely have it, you have it, regardless of what side. So training the "other" side isn't that important in my opinion.
EDIT: Sorry I didn't realize that this was in the Filipino MA forum. However, I still stand by my opinions.
I train my right hand more, but not exclusively. When Prof. Presas was alive he emphasized training both hands, and I study Doce Pares with an instructor who pedantically insists on it, but for myself, I think the strong hand should be emphasized. See also this discussion on FMATalk.com.
I won't vote since the section isnt anything I know anything about, but I train both sides as equally as I can, and right now my right is a bit better, which is odd because I'm left handed.
When I started my left was better but that's changed. I've written it off to my kicks being better on the right because I'm balancing on my left, and because I usually fight right side forward to accomodate everyone else. My reverse punches are definitely stronger on the left though, as are my sidekicks.