Google and yahoo are different search engine and have different algorithm to optimization. Google always try to show quality links in backlinks whereas yahoo show all links as backlinks. First find out which search engine in popular in your country or area and do work according to that. According to me google is the major search engine and have best market in all prospectus. find main traffic driven keywords and optimize them with getting more relevant and quality links.
Yahoo shows you all the backlinks they have found for your website. Google always shows less. I have never really came across the exact explanation of what kinds of websites google shows. It may be just the websites with a particular PR or it a certain link quality. However, Google knows about more websites that link to you than what it actually shows you.
How do you check your backlink anyway? Do you use the link command in google? Better use Google Webmaster Tools so you can see all your backlinks in Google.