I really like Captain Kirk and have always been a fan. But when it comes right down to it, Picard is the better of the two. There are many reason why. Picard is just a better captain overall. He is fit for the job more so than Captain Kirk is. It is more evident now that Kirk is not in the series. The acting techniques behind Picard are nothing short of amazing. He is also more by the books which can be helpful in many ways. He is more willing to actually work with the crew which is priceless. He treats every situation different and that is good.
I don't take lightly that Captain Kirk was absolutely wonderful but he is being overruled because Picard is genius. He had a lot to live up to and he has done that...and more. Coming in and having to fill such big shoes isn't easy but he did it and even rose higher in the calling which is stunning. I have a whole new respect for him and that will never change no matter how I love Captain Kirk.
This question is the outcome of an advertising gimmick by a TV magazine. wanting to draw interest from Star Trek fans it had a painting on its cover by Kinuko Y. Craft showing the two Captains. This anniversary tie-in became a special "hook" to excite reader interest and increase sales. Pitching the "Kirk vs. Picard" competition idea took off. Neither is 'better' they both have their personalities and skills, but causing anger by some individuals favouring one over the other has been brilliant for sales.