What is better: a video camera or DSLR?

I'm looking at buying either the Nikon D3200, canon t3i, or a video camera. I would mainly use to take videos. Although still shots would be nice too.

I've read lots of opinions on this question. Most people have said that a DSLR is the new way to film videos. Apparently they give a more professional look and give you more options. I'm wondering if there are any specific advantages a DSLR has over a video camera or vice versa.

Any other HD video cameras or DSLRs to consider besides the two mentioned above. Also, if I got a DSLR or a video camera, would a plug in audio mic be a good idea?

Stills: DSLR
Video: Camcorder