SERP and PR are 2 different things, so if you have a very good PR it's not sure that you will list on Google/Bing/Yahoo first page.
My sites generally, with one or two exceptions rank higher in Google than Bing but I use bing as a search engine because i got sick of the privacy worries with google. I actually find Bing's search results far more relevant than Googles. especially with googles passion for dropping valuable sites from their main result pages for no good reason (Template monster, BMW, Google japan etc)
I personally put my energy into Google rankings - Bing doesn't appear to bring more traffic, even if you have a better ranking than you do with Google- more people use Google as their SE. Bing doesn't really compete with Google- YET!