I heard that southpaws have shorter lifespans. <_<
I'd say that, out of habit, I probably use my right hand more often than my left. But that's mostly for handwriting, which I rarely do anymore (I can't even remember the last time that I did...). I mostly use the keyboard, which is a joint venture for my hands, so... And they should both be of equal strength. Other than that, I think they share equal responsibility for doing certain tasks. For instance, if a door needs to be pushed I use my right hand, and I use my left to pull (since door handles are usually on the right). But I can use my left hand for things that I usually use my right for without much of a problem (for instance, I usually use my mouse with my right hand, but my sister has things placed on her desk for her left hand and I don't move things around whenever I use her computer).
Basically, I'm going to opt for both. My left hand only fails to compete with my right in handwriting, but I can still write with it... It's just more sloppy than my right's already-sloppy work. But that's okay: thank goodness for keyboards.