My engine contains a bit of parts from both places. Some of my choices were simply motivated by a cheaper price. I'm running a Cycle-X 850 OB kit as it was cheaper than an 836 kit. I got my gaskets, adjustable cam gear and a few other parts from Cycle-X; my cam, cylinder studs and a few other parts from APE (as well as a few more parts that I will be ordering).
Here is the basics that I have figured out about the two suppliers:
APE produces and sells a higher end, higher quality product at a higher price.
Cycle-X sells a Good quality product at a good price (I think they buy their cylinder studs from APE, actually).
If you plan on bringing your bike to the track and racing it, you would better off filling the engine with APE products. If it's going to be a street bike with the occasional hot lap through the twisties, then Cycle-X products will work without a hitch.
A lot of it depends on the skill of your engine builder, too. You could spend $5000 in parts and have a sh!t engine that gets beat up by a $500 engine job if the work is sloppy.