Canon vs Nikon is probably the second most common question I get. It is about as valid an argument as Chevy vs Ford. Both Canon and Nikon manufacture excellent cameras. There are other options as well such as the Sony Alpha series.
There are a few things to consider. As a rule Nikon preforms slightly better in low light, less sensor noise. Canon performs slightly better for high speed subject matter like sports with faster frame rates and slightly better auto focus tracking. But the performance differences are very minor.
The main thing you should consider is how does it feel, do the controls and menus make sense, and does it have the options you are looking for? I am a Canon shooter. This is because I learned on Canon cameras, and now I am very invested in Canon specific lenses and speedlites. When I buy a point and shoot camera I look at Canon first because the controls and menus are very similar, this saves me learning a new system. However the last point and shoot camera I purchased was a Panasonic. Geotagging was a very important feature - really the reason I replaced my old Canon A630. The Canon model at that time preformed very poorly, it was slow to locate its position and the battery life while the GPS was operating was about 30-40 minutes so the feature I was buying the camera for was essentially useless, where as the Panasonic was giving me about 8 hours, a couple of hundred shutter releases and faster positioning.
Yes I bought both and took back the one I did not like, this can be a good strategy if you are unsure what to buy, it lets you experiment with both for a week or so. In my case I bought the Canon expecting it to preform and when It did not I took it back and bought the Panasonic. Fortunately the Panasonic did preform because at the time I did not really have any other options.
If you are looking for point and shoot Cameras there will likely be 6-8 manufacturers making cameras with the options you want in your price range. It is worth researching all of them. At this time there are really only 3 options for DSLRs: Canon, Nikon and Sony. There are other manufacturers but they are not widely supported or as readily available making them much less practical. Sony is definitely worth a look and is the only one of the three that offers geotagging, though Canon is due to release the 6D which is a full frame camera with GPS, WIFI, and uses SD memory. Brining many of the advantages of the Sony series to the Canon line. Features which can be a very handy, especially if you travel. You may feel like this leaves you with more questions then answers, but hopefully now you will know which questions you should be asking.