The problem with these kind of SEO reporting tools is that they are build on stats which have gotten progressively more inaccurate over time. The Yahoo backlink counts are now missing up to 95% of the actual backlinks, even though these SEO tools use this information as if it were the last word on what links a site possessed. To get the real truth on backlinks you have to use a paid service like MajesticSEO dot com. For SEO Elite type of analysis, I find the free SEO Quake browser add-on (the Firefox version) to be a sufficient substitute. If you really are in an SEO death battle with another site in a competitive niche, you either need to use a tool like Majestic to find out what links the other site has and get them too, or take the Russian army approach and just go for broke and massively out-backlink them. For either of these, you may need automated help like Scrapebox, SENuke or, for really difficult cases, xrumer, which is sort of like using a nuclear weapon. SEO Quake will give you some idea of what level of problem you are dealing with and which type of tool will be require to overcome the competitor.