I would say for up close (front door) lower res would allow ID of a person's face etc.
If you are looking at a parking lot, higher resolution would be needed. the longer the distance the more resolution I would want. It would give you better ability to zoom on images to read license plate numbers, hopefully ID faces etc.
I know there are some site/links where people show various levels of resolution, particularly in reading license plates etc. I'd look into that, and figure out what distances you are looking at.
More resolution is better. But also costs more and will limit storage space.
Personally, I hate when you see security cam footage on the news and it is so grainy that there is no way you could recognize someone. I think the goal should be to allow the police to ID a car/person and make an arrest if there is a crime (so I would say go 3-4MP)... Really all comes down to budget.