Google CEO Eric Schmidt Jan. 20 gracefully announced he was handing his CEO role to Google Co-founder Larry Page, the man whom Schmidt took over for in 2001. The symmetry is uncanny. One decade ago, Google was at a crossroads. It was growing traffic, but Page and Co-founder Sergey Brin were being hounded by their financial backers to install a leader with business savvy. They ultimately tabbed Schmidt and Google went on to carve out a place in Internet lore that is unmatched. Yet while the company is the undisputed leader in search and search ads, the company is facing steep competition on the mobile Web front from Apple, which is carving out a powerful handheld force with the iPhone and iPad tablet computers. Under Schmidt, Google has delivered Android to counter iPhone and the iPad might. But the other area where Google is significantly more disadvantaged is in social networking, where Facebook is the dominant power. Google reportedly has big plans to infuse its Web applications with social services, but they have yet to materialize under Schmidt, which many see as a failing. In this slide show, eWEEK takes a look at the potential impact of Schmidt turning over control of the multi-billion-dollar company he helped build to Page, who hasn’t led in years. – …