I grew up with and do both casting & spinning conventionally (cast with right for both, switch to reel for casting). For me, I have noticed a preference of using the dominant hand per technique.
For example, when using the rod to impart action to a lure and just use the reel to pick up line (jerkbaits, Ned rigs, etc), I prefer spinning equipment. Using my dominant hand on the rod, I feel in complete control of the lure and am able to impart whatever twitches or motion I want.
However, for most moving lures such as crankbaits, buzzbaits and the such, I impart more action to the lure using the reel. Having my dominant hand on the reel works better for me, especially since the rod is basically held in place and the hooksets are more of a sweep than a step back hammer.
As a disclaimer, I am the most anti-ambidextrous person in the world. Using my right (dominant) hand, I have a very fluid golf swing, jump shot and bowling delivery. Using my left hand, attempting those same actions make me look like I have a physical disability. The preferences I have most likely don't apply to those who have skills with their less dominant side.