Advertising, no contest. Annoying, intrusive ads I have no qualms about adblocking, because they will never actually get me to buy a product. Helpful, non-invasive ads and clearly disclosed affiliate links? Feel free, since I'm getting some benefit too. There is no way for me to benefit from you using my cpu (ignoring the actual content in this comparison, obviously).

I'm sure any embeddable bitcoin miner will be added to adblock pretty quickly, so you won't have to worry.

Would it change your mind if you were given a portion of the bitcoins generated while you were on a site that was doing this?

For some people, yes. For me personally, no. I find them interesting, but I'm not investing in them really.

I think the best way to do it would be to ask, and be very clear about what you're doing. Some people would gladly help you, but others may be more wary.

Heres how I would do it: have a Bitcoin Plus (or whatever) widget box clearly visible on the website. Have it tell the user exactly what it is doing, including the current speed. Highlight the fact that it is an alternative to advertisement and that it only uses idle processing time (or if its used together with advertisement, state that its used to help pay for the site). Finally, provide a stop/pause button so that if it really annoys somebody or actually is causing cpu spikes, its easy to turn off.