This is a bit odd for me to answer, because I really like both. I have more experience with Spyderco and have always had nothing but good luck with them. I only used the warranty once with no problem and the knife in question got to the Warranty Dept. by my use(mis-use), not any defects. I've had 15-20 Spydies and no issues. I've only had 4 BMs and I had a problem with one in that the scales weren't attached with long enough screws, causing the knife to split apart. I was told by the Warrant Dept. it was a recall issue, so I should send it back ,at my expense. I didn't feel it was my responsibility to pay for this, so I ended up trading it to a friend who thought he could fix it. This was my first BM and I didn't get another for about five years. Now that I have had a couple more, I think it was fairly isolated in terms of quality.
I like the designs of BM as a whole but think they are somewhat bland(maybe not the right word), so if you like one , you'll probably like most of them.
I think Spyderco is more innovative overall. Let's be honest, they pretty much started the trend of one-handed knives, clips and serrations, at least to the masses, anyways. Everyone else pretty much followed. Some of their designs don't appeal to me at all, but I respect the company for not staying in their comfort zone and pushing limits.
I'll give my nod to Spyderco, eventhough there's a BM and a Spydie in my pocket right now.