Let me tell you why people still use Google more than Bing. The basic difference is drawn with the search results. Bing acts as the subsidiary to the giant browser Google, and fetches almost all the data from there. Google, on the other hand, is the master to facilitate the long & complex searches and it is guaranteed that no matter what you have typed there, you will get some relevant results out of your search. Moreover, the server of Google is extremely strong and rarely ditches you. Even, the search results are displayed within the fraction of seconds.
Along with Browser, Google offers a lot of other services such as the Google Adwords, Gmail & Google Buzz.
Now, it's up to your decision to choose the best browser for you. Well, in addition, there are few more browsers to keep in mind like Baidu, Yahoo, Safari, BuzzSumo, Technorati & so on. You can always check them out too.