It depends on how the developer has written the application. Some apps you can choose close and it just leaves it running in the background. This can be bad for your device's memory. Exit always means the program will be shut down. This is a better option if given the choice between leaving it running in the background.
This is a better option if given the choice between leaving it running in the background.
Well that depends too... if it's an auto-updating weather app or an audio app that you want to keep playing in the background, close is the better choice if both are in there.
Exiting many applications will sign you out of active services (such as youmail). I generally close out of all of my programs and I have a very minimal (10-15% max) app memory depletion throughout the course of the day