The age old argument of Nikon vs Canon has lived on through the change from film to digital, and now hits the age of DSLR HD video. Lets for a moment ignore the other makes, such as panasonic, sony, olympus, pentax etc, and focus on the two. Why choose these two over others...well, I suppose historically, this is because Canon and Nikon dominated the lens market, and this meant that photographers could use their old film lenses on these new DSLRs. Lots of companies are coming out with quite good cameras, some of which can rival some of the Nikon and Canon cameras. I'm not mentioning such cameras as phase 1 and Hasselblad, which are out of my price range, and really for high end photography (eg. pro studio work).
One major issue is compatibility with other lenses. Being a Nikon D40X owner, I was partially victim to this, since in many instances, AF does not work with the D40X, which lacks its own focusing motor. However, this small limitation is nothing compared to the EOS dilemma witnessed on Canon's mounts. Rendering all FD manual focus lenses impotent on the new mounts, a lot of lenses became extinct! If you are starting out as a new photographer, then this issue is redundant (unless you happen to be inheriting lenses).
Now some more technical issues:
Traditionally, Canon were used by sports and action photographers because of the speed of autofocus, but Nikon are now equal in the expensive high end lenses. In cheap lenses, there still seems to be a little bit of difference. There is a bit of a rumour going round that Canon are still dominating this market, however, this could be due to the huge amount of money they put into advertising and marketing, as well as the fact that L-series lenses (which are bright white) are so easily picked out in a crowd. The sudden move of wildlife photographer Andy Rouse would say otherwise, praising the D3's high ISO performance, and consistent AF.
Flash control is a lot better in the Nikon camera, where Canon hides a lot of functions in its warren of menus. In TTL, Nikon flashes present information in an easy way, and the photographer has complete control over each independent flash. In this respect, Canon has an advantage where a quick turn of a dial can change the entire flash exposure quickly and simply. Nikon also carry an on camera wireless system, where Canon forces you to buy a pocketwizard.
In Nikons, there are only 2 sensor sizes: Full frame and 1.5x, whereas Canon has full frame, 1.3x and 1.6x. if you're going to use different lenses on different cameras, this can be annoying, as they each perform differently depending on the frame size (full frame being very wide, while cropped zooms in). Full frame tend to be more expensive as well, though I think the quality of image and wide angle ability is well worth a look.
I could talk about the differences in image quality and lenses for a quite a while, however, my next point is going to by about video. There are a few reasons why Canon video is generally considered better than Nikon. To avoid European Taxes placed on camcorders, Canon placed a limit of 12 minutes on any single clip (this might also be to do with buffering space on camera). In comparison to this, Nikon only have 5 minutes, which, having recorded lots of interviews, is not particularly helpful. There is no 1080p on Nikon video, which for most situations is OK, but soon, this will be the min requirement for HD. The quality of the two codecs is incomparable. The Canon H.264 beats the Nikons m.peg every time.
Finally, comes personal choice. I started on Nikon cameras, and while I learnt photography with this set up, I also think that the Nikon camera is set in a much more user friendly way. All the controls seem to be in the right places, from the on off button to changing apertures and shutter speeds. I have found that the AF speed on cameras is generally pretty similar, though on my D40X (my first camera), I had the problem of lens compatibility. If I was going into photography, I would certainly choose a Nikon camera, starting out on a cheap model, say the D70, moving to a more pro camera, possibly the D3 or go to medium and large format. The inclusion of such good quality HD video on the Canons has forced my hand, and I am currently using a 7D to shoot video. Aside from the slightly annoying controls, and somewhat convoluted menu system, I haven't got any major issues using it, except, I have to get all new lenses, or an adapter.
Cameras are largely down to consumer choice and feel. The best thing to do is go into a shop (Tottenham Court Road has quite a few camera shops, and you might be able to bargain and get a good deal), and try a few cameras out. I will probably blog about lenses at some point, but kit lenses tend to be pretty useful, and a lens like the Nikon 18-200mm VR is always quite good. If you are saving up, I quite like a 100mm macro, which encompasses portraits and macro work. Fixed focal lengths or prime lenses tend to be better quality, but only if you are going into photography as a profession, otherwise, there are a lot of good zoom lenses out there, including other third party companies, like sigma and tamron.
Canon and Nikon are both massive multi million companies, who seem to leapfrog each other each year. At the moment, i would choose Nikon for photography just, but Canon in video by a long way, but this could change at any instant!