Different search engines follows different ranking standard, initially you have to focus both factors on your website. Like wise Google love to rank your webiste if it is informative and following proper guidelines of Google like unique hand crafted meta tags (Title and Description) while Bing also giving priority of Keywords tag. Google rank your webiste well if you used diversify keywords as hyperlink but Bing love if you build links on exact match keywords.
Read more about Bing guidelines on Internets how to optimize site for bing search engine.
For Google everything is known.
Bing also important factor as 70% shares of search Google aquired, but 30% share is of Yahoo and Bing. Since yahoo and Bing are same and using same ranking factor so no need to focus individually.