Analog Pros:
Cost: Analog cameras generally have a better price to performance ratio compared to IP in residential applications.
Flexibility of design: There are many varieties of camera types, from small covert cameras to indoor domes. This can make fulfilling your goals easier by using a camera designed for your specific application.
Compatibility: This makes it easy to use existing cameras or mix and match vendors for equipment.
Maturity: Analog systems have been around longer and many of the earlier generation problems have been worked out.
Analog Cons:
No bells and whistles: Analog cameras don't have some of the features like built in digital zoom that IP have, except at the highest price points.
Interference: Wireless Analog cameras have problems with interference and are unencrypted. Anyone can view the signal.
IP Pros:
Range: IP cameras get a better image over long distances (depending on the resolution).
Larger applications: You can use fewer cameras to cover a large area.
Better Picture: IP cameras can offer a superior image depending on the resolution level.
Zoom: You can zoom in and focus on a concentrated area of interest. (Like the license plate cameras on the traffic lights).
IP Cons:
High bandwidth use: This system can weigh down your network. (Depending on the system you choose).
Cost: IP cameras cost more than comparable analog cameras.
Expandability: It is not as easy to mix, match, and expand an IP system. The software and camera compatibility can lock you in with a specific vendor.