I'm a beginner but I'm starting fast.

I recommend D3200, an update of D3100.  Better sensor than D3100 and can also do WIFI transfer from the camera.  Has excellent video features; 1080p HD at 24,25, and 30 FPS. Not much more expensive and comes with excellent 18-55mm kit lens. 

Video is awesome with 10x digital zoom without noticable loss of quality

http://snapsort.com/compare/Canon-600d-vs-Nikon_D3100

The best for all starters. All possible options, great photo and video quality. Highly recommended.

You said, you are going to use for many, many years....which means, during that time, you are going to buy lenses. Then I would recommend T3i. There are bunch of lenses out there, and they are easily usable with adapter for canon DSLR. But those lenses for Nikon are a little bit hard to use. But if you already are familier with Nikon system and lens, then, of course you got to buy Nikon. 

Since Ameera wants a camera that she expects to use for many years to come, the Canon T3i is ideal for her purpose because it is a fairly new release model compared to Nikon D3100.

If filmography is your calling, then go with the T3i. Trust me. 

Thy are easy to use. I have used Canon's for many many years. I have tried Nikon they are not easy to use & they don't last. 

Nikon have better cheaper lenses and some of them even don't have a Canon version, for example the 18-105mm and 35mm f/1.8.