I have also heard of one hemisphere being called "divergent" and one "convergent". This may not make any more sense than emotional vs logical, but it does hint at how you might model it more easily. I don't know how the brain achieves some of the impressive computational feats it does, but I wouldn't be very surprised if all revolved around balance, but maybe that is just one of the baises you have when you are a brain with two hemipheres (or any even number) :D
A balance between convergence and divergence is the crux of the creativity inherent in evolution. Replicating this with neural nets sounds promising to me. Suppose you make one learning system that generalizes and keeps representations of only the typical groups of patterns it is shown. Then you take another and make it generate all the in-betweens and mutants of the patterns it is shown. Then you feed them to eachother in a circle, and poof, you have made something really interesting!