The picture taking ability and quality is about equal on any of the three cameras.
So that leaves features.
Since you are interested in video - the Nikon D5100 is your better choice.
It has continuous Focus, the others do not.
The other cameras get into trouble if you are making a video of an object coming toward you or away from you.
Depending upon the available light, the moving object could become out of focus as it get further away/close to the camera.
If you are really into video, you should be looking for a camcorder.
Canon and Nikon have announced future digital DSLR cameras that work very well as still and video combination cameras.
The problem is: not available until next year and the price is from $9,000 through $20,000.
..
I have been using two of the entry level dslr pentax kr and canon t3,both are nice cameras, picture quality about the same,pentax shoots faster and it is heavier,"feels" better build.If you are going to make that kind of investment, would you go with one of those two or expend couple of hundred dollars more and go with nikon 5100, for the extra features,1080p record mode with auto focus,articulated lcd...(my budget is around 750)

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