[Nexus 6P Q&A, Help & Troubleshooting] AJerman:
Well, since I just sold my Note 5 for the 6P, I guess my answer would be the 6P.

I just got it today, so my experience with the 6P is somewhat limited but here are my thoughts (I'll leave the price difference out of it, but that's obviously a huge factor as well):

The Note 5 is probably the BEST phone on the market right now, period. Features, power, design, it has everything. Everything except being a Nexus and running stock Android. This means the 6P has a noticeably smoother and, in my opinion, better UI. The Exynos CPU is undoubtedly faster. This is most noticeable when launching apps. The Note 5 will definitely beat the 6P there. That said, would you even notice if you didn't have them side by side? Probably not. The Snapdragon 810 is no slouch and nothing feels slow when you're using the phone. So to me, the Note 5 has an overall negligible edge on power when it comes to actual use. As for the multitasking capabilities mentioned above, unless you mean the split screen which usually seemed like little more than a gimmick to me, the multitasking is pretty bad on the Note 5. It has an extra GB of memory, and yet it still constantly kills apps. Hopefully Samsung tweaks that more with future updates because I feel the 6P probably has the advantage in multitasking at the moment.

The Note 5 also has a slightly better screen. They say they are the same panel, but I suspect either Huawei gets the slightly lower quality screens of the two, or Samsung still has some tricks up their sleeve to optimize their own screen, or probably a little of both. That would explain the number of screen complaints on the 6P while the panel is still relatively new to production. Again, assuming you don't get a pink screen like some, the screen still looks every bit as good for the most part. I can't imagine anyone complaining about a good 6P screen. Samsung has a brightness setting called The Face of the Sun which I don't miss forgetting to turn back to adaptive before looking at the phone in the middle of the night. I haven't really used the phone when it was really bright outside yet, so I can't say for sure if I miss the extra brightness there, but again I have no complaints about the 6P.

The camera is also better in the Note 5, but the 6P's is pretty damn good too, and if you care that much, get a real camera and stop trying to take pictures on your phone. That's pretty much the end of that discussion for me. The main reason I got the Note 5 was because Samsung finally designed a nice phone again, but again, the 6P feels equally premium. In fact, while I respected the design of the Note 5 and wanted to like it, I kind of didn't. Something about the feel of it just never felt quite right to me. I still think a glass back on a phone is stupid, just like it was when Apple did it and learned their lesson. I very much like the look and feel of the 6P, especially the Frost version that I have. The back of the Note 5 is too rounded and it makes the already slippery glass back feel like a bar of soap in your hand. Oh, and one last feature that was actually pretty important to me on the Note 5 was the wireless charging. Too bad it doesn't work half the time.

Now, onto the 6P. Like I said, the 6P has more than enough processing power, a more than good enough camera and screen (again assuming a good one), and a fantastic design and feel. Remember that sinking feeling you got when that first 6P pic leaked? It's light years better in person. I really do like the design of this phone. It reminds me of my One which was one of my favorite phones. Being that we are all here on XDA, the advantage of the 6P is that it DOESN'T have the Exynos processor. I had the Note 5 less than a month and was already getting annoyed that I would never be able to have anything but the stock software or small mods on top of it. Touchwiz was incredibly better since I last saw it, but it's still pretty ugly, in particular the notification drawer in the Note 5 really bugged me compared to stock Android. Because of all this, the smoothness of the 6P makes it feel like a faster device during normal use. You'd never know it was a little slower without having them side by side. And of course, there's always the time difference in receiving updates. Sure you'll get Marshmallow on the Note 5, and probably pretty soon. But every update after that will start getting more questionable and probably slower as other phones become their priority.

So in conclusion/tl;dr, they are both at the very top of the list of best phones on the market. The speed differences aren't something you'd ever even know most of the time without directly comparing them, and you'd be forgiven to think the 6P might even be faster. They both top the list in nearly every category. I can't imagine anyone being disappointed in either phone. If you value any of the Samsung specific bits like the stylus, then the Samsung is for you. If you value the ability to modify the software on your phone and receive updates as soon as they are available, the 6P is for you. If you have either, consider yourself lucky to have one of the best phones on the market. I switched because I wanted to be able to use real ROMs and kernels, not just the tease you get with an Exynos device, and I wanted updates ASAP, even as previews. I suspect most people who are here on XDA probably value this as well, which is fairly evident by the fact that a month newer device has WAY more activity on here.