yeah, my default search engine is bing. But sometimes you have the feeling it probably has less stuff in its database than what baidu has crawled and collected. Out of habit I rarely use 360 or sogou so I don't know how they fair compared to baidu or bing.
Yeah, I've found Bing to the best option when I'm in the mainland, only because all the local search are even more terrible at english.
When I need to search in Chinese, baidu is the least terrible (but still really bad). Sogou isn't too far behind, but it's index is not as fresh, in my experience.