The 3 criterion I consider in choosing a digital camera is image quality, lens range and physical size.
If image quality is your number one criteria, get a digital SLR because they have larger sensors than smaller digital cameras. This is the most important factor affecting image quality because the size of the sensor dictates the size of the pixels captured by the camera. So a 12 megapixel point & shoot with a 1/2.5" sensor is going to give you poorer quality images than a 12 megapixel digital SLR with an APS-C sensor.
|Medium format||50.7 x 39 mm||High-end Pro digital medium format|
|Full frame||36 x 24 mm||High-end Pro DSLRs|
|APS-C||24 x 16 mm||Prosumer-based DSLRs|
|4/3"||17.3 x 13 mm||Four Thirds System|
|1/1.8"||7.2 x 5.3 mm||High-end compact cameras|
|1/2.5"||5.3 x 4.0 mm||Consumer-based compact cameras and high-end cellphone cameras|
Table (from http://www.engadget.com/2011/12/16/engadget-primed-why-your-cameras-sensor-size-matters)
In conjunction with the larger sensor, the image processor also matters. This is more of a factor for smaller sensors because typically large sensor cameras will already have very good digital processing. So if you're considering a camera with a small sensor, look for one that also offers better digital processing to improve the image quality from that smaller sensor. If you need to find the sensor size and image processor for a camera you're considering, go to DPReview's camera database where they provide the specs of cameras including the sensor size and image processor.
Getting a good lens range allows you to capture images near and far. Wide lenses allow you to capture group pictures from within short distances and telephoto lenses allow you to capture intimate pictures from long distances. My recommendation is to look for a zoom lens that starts at 24mm (or lower) on the wide size and goes up to 200mm (or higher) on the telephoto side. You can get this range from many point & shoots and from digital SLR lenses today.
But if you want the widest and farthest lens range, the superzoom cameras are the ones that deliver. The longest superzoom on the market today (Nikon P510) delivers a lens equivalent of 24 -1000mm.
With the advent of smart phones, portability of cameras has become a primary factor. I know many people who have nice DSLRs yet leave them home when they go on vacation in favor of their point & shoot or their iPhone. The most portable cameras are still the point & shoots and some are thin and small enough (e.g. Canon Elph 300) to easily fit in your pocket.
Putting it all together --- Combination of Factors
So given the 3 criterion, what if you want a combination of all of these factors? Well for one, you cannot have a digital SLR and have portability. They are just too big for comfort. One option to consider is a bridge camera (e.g. Fuji Finepix HS30). These are cameras that look and feel like digital SLRs but are smaller and don't have removable lenses. Or get a high-end compact camera (e.g. Canon PowerShot G1 X) that combines a large sensor in a portable camera body. And there are also the mirror-less cameras from Sony (NEX-7) and Nikon (1 V1) that are smaller but give you the option of removable lenses.
Ultimately the key question to consider is will a camera allow you to capture the images you want?
Portability is great because you can take the camera anywhere, but there's a reason why sports photographers still use digital SLRs and that is because the design and speed of a digital SLR will allow you to capture moments in a way not possible with a point & shoot. But again, if size and weight is an issue, some bridge cameras will give you the design and speed of a digital SLR so capturing those moments will be possible, but because bridge cameras will likely not have the large sensors that digital SLRs have, you will sacrifice on image quality.
There's also a reason why studio photographers use high-end digital SLRs and that is because the large sensors give them the ultimate flexibility they need in capturing images at the quality their clients expect and need. But these studio photographers also don't need to carry around their camera all day at Disneyworld.
In this Engadget Primed article on sensors, Sean Arababi describes an interview with Annie Leibovitz:
Annie Leibovitz when asked what kind of camera one should buy, remarked the iPhone – “that is the snapshot camera of today… it’s the wallet with the family pictures in it.” Although I truly dig the iPhone 4S’ new 8 megapixel camera and all the revolutionary technology crammed into the smartphone, the Sony-made image sensor is just not large enough to rival images captured with a DSLR – and that’s expected. Apple describes its A5 chip, designed with an image signal processor, as “just as good as the ones found in DSLR cameras” and this might be true, but the image sensor is not – big difference between a signal processor and a sensor. It might allow you to shoot faster, or capture nice color and tonal range, or to use when you don’t have a camera handy, but it can’t match the quality of a larger image sensor that’s comes with a higher-quality lens. Simply put, you can’t squeeze a V8 engine into a moped. Then again, I can’t make a call, text, tweet, Google Map a route, or play Fruit Ninja with my DSLR camera, either.