The Big Differences
...And why you'll want to stick with one brand.
If you're serious about photography, or would just like to have a nice camera to take pictures of the family during vacation, then there will come a time when you'll probably want to head to your nearest store or online retailer and pickup a nice DSLR. However, there are a million brands out there all offering pretty similar technology. It's a tough decision to make as consumer as camera's are not cheap. There are, of course, a few ways you can be sure you're getting all the bang for your buck.
One such way would to Do your due diligence! Even this article may not be informative enough for you to decide what you want so look around and know what you're searching for. Another important, and perhaps a bit simpler way, would be to let capitalism do the research for you and settle on a brand that's know for its quality and cost effectiveness. The problem here, however, is that that narrows it down to two, huge, brands. Canon or Nikon.
Why do I have to choose?
A great question with a simple answer. Each brand of DSLR has its own patented way of attaching a lens to the camera body. In other words, the lens of one brand is not interchangeable with the lens of another. Though, technically nothing is stopping you from buying both a canon and Nikon, it doesn't make very much sense.
As you can see, they're both very fine brands!
Canon or Nikon
Advantages of Canon:
Canon is considered the more user-friendly of the two brands. The cameras are often very to the point and it's pretty easy to just pickup and take some nice pictures. That's not to say that you can't do the same with a Nikon, however the learning curve is a bit steeper with Nikons. Aside from that, It's also important to note that Canon will be a bit lighter on the wallet if you decide to really kick off your photography and buy a few more Lenses. Though, as far as variety is concerned, they have about the same number of lenses. Overall Canon will be easier to start with.
Advantages of Nikon:
Nikon, on the other hand, would be a bit harder to begin with as the user interface is a little more advance. However it's probably not incorrect to say that the differences in interface are near negligible once you've really figured out how to use a DSLR. Nikons true advantage is probably a bit of a lead in technology however it's not at all uncommon to see professionals using both Canon's and Nikons for their various needs. I think it's also fair to mention that Nikon is perhaps considered the flashier of the two brands, and that it really prides itself in its equipment. I think someone with a heavy interest in photography may want to start with a Nikon to get a better feel for how a camera works.
Ultimately, what you decide will not make a huge difference as long as you keep the same end goal in mind. That's to say, it's not a bad decision to buy a Nikon for your family get togethers, especially if you want to take some nicer pictures on the side. Nor is it a terrible idea to buy a Canon for professional use, as the nicer lenses are often considerably cheaper than their Nikon equivalents. It's a hard decision but hopefully I've helped you come to a reasonable conclusion.