Andrew B.:
So he doesn't say that they're identical, just that they're directly related. From what you guys have said, I guess that would be in the sense that both practices help turn off the discursive mind and see reality directly (frustratingly, that seems to be exactly the opposite of what noting does for me. But then, maybe I'm just doing it wrong).
No need to be frustrated, just use whatever techniques suit you best, right now. The point is just to perceive reality clearly, whether it's the 3 characteristics in sensations, or the 5 aggregates, or the 4 elements, or the links of dependent origination, or whatever.
Also, a distinction to make: noting
ties up the discursive mind, i.e., occupies it, while a koan (from what I understand)
interrupts it with confusion. Samadhi, on the other hand,
subdues it (turns it off). I also like Christian's comparison between sensate observation and using koans to interrupt
conceptual thinking (as opposed to merely
discursive thinking).
If noting isn't working for you, you could also try different types of noting. You can do descriptive noting ("tingling, tightening, softness, brightness, discomfort, scraping, pain, chirping, squeaking, ..."), which requires more cognitive resources, or 6-sense door noting ("thinking, hearing, hearing, seeing, ...") which requires less. Or you can just notice without the words. I've heard that different types are helpful at different stages of practice too, although some teachers might try to have you just use one style.
Take a look at:
http://thehamiltonproject.blogspot.com/2011/02/yogi-toolbox-detailed-noting.html
I think everybody customizes their noting techniques for themselves based on reading, experimentation, their own ingenuity, and where they are in their practice.
As far as my personal experiences with koans go, and even though I've had some difficulty figuring out exactly what to do with them, it was a koan that got me into my A&P. But it seems almost to have been a fluke. I asked myself the koan, and instead of trying to figure it out, I surrendered to it. The rest happened automatically. But it was all so sudden and jarring, and frankly a little terrifying, that I don't think I really experienced the clarity of insight that a lot of people on here seem to report after their A&P events. Go figure.
No problem, your path is your own! Sounds good to me. Keep experimenting, learning. It's trial-and-error.