First of all, I try not to forget that, beneath all the bull, pedigrees are there for a reason. They show you what you have a good chance of getting (although I firmly believe that nothing can tell you 100% what you're in for.)
If I was looking at a horse which I intended to breed, I would be hard put to say that I would ONLY go for one or the other- good conformation might have been a stroke of luck, you don't know exactly what's going to pop out in a year, or at least not as well as you would if you could see the horse's ancestry. Bloodlines are created for that reason- to preserve traits which are desirable and save you a bit on the guessing.
But, if you breed a poorly conformed horse because of it's bloodlines, you're an idiot.
Overall, when breeding is involved, I think that if you don't have good confo and a good pedigree, don't breed.
And so, personally I would choose conformation over pedigree, without doubt, because
1.) I am not interested in breeding. I am not a huge fan of mares, a stallion is useless if he's not breeding, and raising a foal appeals to me only slightly more than raising a human child- it's a ton of work, it takes ten times more patience than I have, and only wins out against a human kid because let's face it, foals are a hell of a lot cuter and they can be sold if you don't want them anymore, lol.
2.) I don't favor standing over a broken down horse, pointing at his pedigree, and saying "he may not have amounted to anything but LOOK AT WHO HIS GRAND DADDY IS." Nope, not this gal.
3.) I don't do anything that requires a pretty pedigree, and the things I plan on doing in the future put conformation before it anyway. I want a nice sturdy horse (preferably a gelding) that will be my partner in crime until he's thirty.
Summary: Conformation for me.