I own one disc and one rim brake bike. I find it mildly frustrating that I can't use the same wheelsets on both bikes.
This problem really becomes apparent if you're shopping for a new set of fancy wheels. You have to decide which bike they will be used on. It's like deciding which of your children you like better.

Beyond rim/disc, I wouldn't worry about other components being matched. I can't really imagine a scenario where I'd be swapping other components.