Another important difference is that some of the smaller board models does not have the FTDI chip on board. It is the FTDI chip that creates the virtual serial port used to communicate with a PC/Mac/whatever when putting the program on the ATmega processor or when the program is running.
These boards require that you buy a special cable or converter that has the FTDI chip in it. This cable can then be used with any number of the FTDI chip less boards.
The advantage is that the boards are smaller and cheaper without the FTDI chip.
Also some of the boards run at 3.3 volt as opposed to the 5 volts that the "standard board" uses.
If you are just starting up and want to experiment and learn i suggest you go for the standard board, or one of the clones with the same layout / functionality. This will make it easier to use the available shields.
If you have a specific project, then you should evaluate your needs, and think about things like how much space do you have?, how fequently are you going to reprogram the board?, will the board need to communicate with a PC other than for being reprogrammed? what voltage is present in your project to drive the board?