The D5100 and T3i are both great for photo and video. The T3i has an edge over the D5100 in the video section, while the D5100 is also a good option to consider for photo. Costco has good DSLR kits for each, both for about 900 dollars, and both include super-telephoto zooms. You can also buy a body and a telephot lens separately if that is what you wish.
If you plan on doing any slow motion, the T3i, which can record at a framerate twice as fast as the D5100, will get you smoother slow motion(this can also be simulated via the Smooth Video Project software, which is a free frame interpolation software). However, unlike the T3i, the D5100 offers full time video autofocus, which would be useful if you have a subject that is moving around a lot. The T3i has yet another video trick up its sleeve however, and that's digital zoom. It offers lossless digital zoom by using the sensor to its full capabilities. It can boost your lens's zoom by up to 10x, with some loss of resolution at the higher magnifications. The main problem with the D5100's video is difficulty of manual exposure. It's not impossible, but a bit of a kluge to set manual exposure in that you can't change it during live view unless you have a lens with an aperture ring and it automatically sets exposure unless you press the auto-exposure lock button.
For stills, the D5100's sensor is larger and it has better high ISO performance, which shouldn't be of too much of a benefit unless you are shooting surfing in low light(unlikely). The D5100 shoots marginally faster(4 stills per second vs 3.7 on the T3i) and for quite a bit longer without slowing than the T3i, which would benefit you when shooting surfing. The T3i has a built-in focus motor, so any lens made after 1987 will autofocus on it. The D5100 doesn't have a built-in motor, so certain lenses(lenses that aren't designated AF-S) won't focus on it. The D5100 has a few(2) more focus points than the T3i, though I'm not sure how much of a benefit that is. The D5100 has a longer battery life, though I doubt you'll be able to exhaust either on a single day at the beach.
Considering both of these options, I'd go with the D5100. For your needs, it seems best. However, the T3i has quite a few advantages as well. You should consider both choices carefully before making a decision, as you don't want to make one you'll regret.
