My stock MKIII Browning Hi Power is my most accurate centerfire pistol out of many very good ones from various manufacturers. It is the most naturally pointing, although my CZ's, and HK P7's come really close. The P7 is just about as accurate and naturally pointing, but the BHP does have the ability to carry 15 + 1 with flush fit Mec Gar magazines, in a pretty slim, compact package for a service pistol. It just plain works.
Just to clarify, I think many of these pistols have pretty equal mechanical accuracy. The grip, grip angle, trigger, balance are all personal factors and what I may shoot better may not work as well for others. I'd be happy taking any of the above or a 1911, and some others. There are a lot of good alternatives, obviously.