I never really got the whole Dick/Kory thing until the Teen Titans cartoon, but then I can honestly say I never got Kory until it either, so...
I think the thing that does click with me in regards to Dick/Babs is...and I doubt this is the basis of a healthy relationship...together they seem to form one healthy, well-adjusted Batman. Dick is the lone warrior avenging his parents death, Barbara is the reclusive detective sifting through data for answers. Dick's playful enough to pull Barbara away from the keyboard when she's obsessed, and Barbara's forceful enough to knock sense into Dick when he goes to the edge.