Basically there are two types of digicam :
1. Point and shoot digital camera : Small and portable camera with Live Preview capabilities and limited motion video features mostly used for taking Snapshots.
2. dSLR (digital single lens reflex) digital camera: The reflex design scheme is a major difference between a dSLR and an ordinary digital point and shoot camera, which typically exposes the sensor constantly to the light projected by the lens, allowing the camera's screen to be used as an electronic viewfinder.
There is also the Bridge / SLR ( Single Lens Reflex ) digicam often confused for a true dSLR Digicam. It has small sensors and Livepreview just like Point and Shoot digicam and shares a few features with dSLR but it's not a true dSLR.
Points on which dSLR digicam scores over Point and Shoot digicam :
1. Optical viewfinders which tend to be more comfortable and efficient, especially for action photography and in low-light conditions.
2. Accurate preview of framing close to the moment of exposure
3. Larger sensors : similar depths of field and picture angle to film formats.
4. Choose from a variety of interchangeable lenses
5. Less shutter lag, faster autofocus systems, and faster frame rates
6. Ability to attach additional accessories. A good dSLR can really be customised.
Now, points on which Point and Shoot digital camera scores over a dSLR digicam:
1. Generally smaller size and weight.
2. Generally lesser cost and if chosen wisely, a great value for money.
3. Few DSLRs with a video mode, while this has become a standard feature of compact digital cameras.
4. Most DSLR models lack live preview on their LCDs, a nearly universal feature among compact digital cameras (many newer DSLRs do offer this).
5. Noisier (audio) operation, due to the SLR mirror mechanism.
6. Small digicams generally can focus on closer objects than typical DSLR lenses.
Simply put, if you really have keen interest in photography go for a dSLR
Also if you have money to splurge and videos are not a priority then go for a dSLR.
On the other hand if you want to strike a balance between cost and performance go for the compact Point and Shoot digicam. There are some real good ones in 6 MP TO 10 MP range. But as I pointed out in last Tuesday's Tech post, Megapixels are not everything.