Yes, BaK really works. Like Solon said, you have to start feeding it either a few weeks before the summer coat comes in or a few weeks before the winter coat comes in.
I have tried both straight paprika and Nu-Image Dark Horse and haven't found them to be as effective.
I started my mare on Nu-Image around May this year. Her summer coat was already grown in, but it didn't matter because she was already black from the BaK. So if the Nu-Image worked, she should have stayed black and if it didn't work, she should have faded. Well... she immediately faded. I put her back on BaK (this was now about 4 weeks after I started Nu-Image), and so far every scrape she's gotten the hair has grown back jet black. I'll take a picture tomorrow and post it here.
As far as paprika... I found that to be totally ineffective. BaK contains paprika among a lot of other things, including soybean and flaxseed - both of which contain much more copper than paprika does.
Here's what my mare looked early this summer on BaK:
And here she is after just a few weeks of Nu-Image:
I'll come back with the picture of the black regrowth : )