I like all three of them (Connery, Moore, Brosnan). Each for his own style.
Although Connery also tried to play the 'smart'/'womanizer' moments, I never could connect to him being a British gentleman. I see him more like the 'tough guy'.
Moore for me brought a lot over-acted self-irony to the Bond series. To me it feels like he played each scene with an blink of an eye. He fully fullfilled the British gentleman stereotype, but his action scenes weren't as good as Connery's.
Brosnan somehow managed to combine both for me: Connery's 'tough guy' and Moore's 'very british' and he felt right in both cases.
Now, I'm not sure how the different Bonds would work out in the other's stories. But one thing I know for sure: what set the Bond movies apart for me all the time, was the 'britishness' of the hero. With Daniel Craig, we've reached the 'just another Hollywood action hero' stage, making the Bond movies interchangable with a lot of other action movies. I'm not blaming Craig for this, but rather the desperate attempts of the script writers/directors to 'modernize' the franchise. Franchise, a term I read/hear with growing frustration and anger, it's synonymous to 'cater to the (current) masses taste, no experiments, please!'