The Pentax, Canon, and Nikon cameras all feature two separate autofocus systems: traditional phase detect when using the viewfinder and contrast detect in live view mode. They also have extensive video functionality.
The Canon's phase detect autofocus system is lightning-fast. Although its 9 AF points give it a slight disadvantage when shooting moving subjects compared to the other cameras, the autofocus is both fast and accurate for general-purpose shooting. The T4i lacks a dedicated AF assist light, but it can use its built-in flash for this purpose instead.
The T4i's contrast detect autofocus, on the other hand, is quite slow. The camera does, however, support full-time autofocus in video mode, which is a big advantage over the other two cameras but the noise from the focusing motor gets recorded so AF in video mode requires the use of an external microphone.
The Rebel is without a doubt the best camera of the three for shooting video. The articulating screen, full-time autofocus, and external mic input make it ideal for your everyday video needs.
The Nikon has a fast and decisive phase detect AF system, though it's not quite as fast as that of the Canon.
In live view, it's the fastest of the three cameras, and it has a very effective face detection feature, which, unlike that of the Pentax, has a fast enough processor to keep up with rapid movements.
The Nikon's articulating screen comes in handy for shooting video, but it has the most limited array of framerates (see the specification page). Like the Canon, it will accept an external microphone and has full-time video autofocus.
The Pentax, like the Nikon, has 11 autofocus points. Its phase detect is the slowest of the three, but still very good for general-purpose shooting. The difference doesn't become easily noticeable unless you're shooting indoors.
In live view, the K-30 has Pentax's latest-generation contrast detect autofocus, which falls between that of the Canon and the Nikon in terms of speed. One handy feature which the Pentax has but the other cameras lack is focus peaking, which makes it easy to focus manually. This comes in handy with older lenses, as does Pentax's in-body shake reduction.
Compared to earlier Pentax DSLRs, the Pentax K-30 has been upgraded in terms of video. Not only does it support manual video controls like the other two cameras do, but it makes them very easy to change. In addition, like the Canon, it can shoot at 30FPS in full-HD, or 60FPS in 720p. Its video mode is harder to get to, however, and without the articulating LCD screen and external microphone input, some may find it to be a bit limiting.
In this section, the Canon is the clear winner in terms of phase detect AF and video. The Nikon wins when it comes to live view AF.
Neither the Pentax nor the Nikon are perfect for video, though we don't understand why Pentax decided to leave out the external mic jack in a mid-range DSLR. All three cameras have mono sound via their internal microphones.