There are some initial differences which are slowly becoming apparent.
Before you rush to optimize for Bing, keep in mind the Bing algorithm is still being tweaked however below are some of the early differences I have found.
1. Bing appears to give less priority to Keyword Density.
2. Bing seems to give less priority to Link Denisty as well.
3. For Bing domain age is major (this is one of the early algorithms, since their game has just begun and apparently seem to think the domains which have been around a while are to be trusted. In my opinion, this will change).
4. For Bing Anchor texts carry more weight than Google.
5. Social site links are weighted less by Bing
6. Bing weighs in heavier for the H-Tag
I am personally not going to be optimizing specifically for Bing. It is just good to be aware why the SERPs are the way they are. I am going to watch the battle between these two in the coming months and tweak accordingly. At least for now the battle is being fought with ad dollars not with sparkling search results.