Both manufacturers make a range of cameras, all of them have strengths and weaknesses. Just like with vehicles, there is no "best," only "well-suited for what I do" or "not well suited for what I do." Moreover, the suitability is temporal- ~two years ago, Canon had the best low-light imaging cameras of the two, now it's Nikon- but "better" doesn't necessarily mean much- I can get great images from pretty-much any current and past generation DSLR on the market- how much "better" do you need, and how much "better" can you afford?
Right now, the D3x is the king of the hill, but few pros, and few amateurs want to fork out the sort of money that takes- even if the next step up is considerably more money and compromises in different ways- if you believe DXO mark
http://www.dxomark.com/index.php/eng/DxOMark-Sensor then Nikon holds 3 of the top 5 with Phase One holding the other two and Canon coming in sixth and seventh- but that's only applicable to the P65, P40, D3x, D3, D700, 1DsIII and 5DII- it doesn't "trickle down" except in specific ways to lower-end products. So, if you're not spending a few thousand dollars on a camera body, then a few more thousand dollars on lenses to go with it, you're probably looking at the wrong thing.
Together, the two companies hold about 80% of the global DSLR market, with Canon probably still slightly ahead, but losing overall to Nikon in terms of market share gains for the last 3-4 years running. Sony is the next-biggest player with around 8% of the market, everyone else has less than 5% each. This landscape is unlikely to change much in the next 3-4 years even if one or two of the other players go out of business or get sold. The only real player with potential to shake the market in a major way that soon is Samsung- but they seem to be content to try to out-maneuver Olympus in the smaller camera market for the short term and even with their huge retail presence, it'd take a lot of work for them to do anything significant in that timeframe.
Canon is a much larger company than Nikon, and all of the players have multiple lines of business, but with the global economic slump, Nikon has basically moved from optics company to camera company since the majority of their revenues are from digital cameras these days. Nikon's business model recently has focused on low-priced entry-level bodies and multiple lens sales- which has resulted in them closing with Canon for the first time in DSLR sales in their home market- a big metric for Japanese companies.
Neither company makes bad products, and I don't know a photographer who couldn't get pretty equivalent results using relatively equivalent models from either company.
Instead of looking for a "best," you should decide which factors are important to you, what your budget is, and who best fits your budget for those factors that are important. You can modify that with ergonomics between different cameras in each company's line, and future needs- but anyone should be able to easily make the case for either manufacturer unless they have a specific axe to grind.
We'll now return you to your regularly scheduled posting where everyone who shoots something other than Canon or Nikon will chime in about how much value you miss by not going with one of them...
Paul