The fundamental difference between a microATX board and a full ATX board is only in the form factor, i.e., physical size.
An ATX board, being larger, has more space and usually has more expansion slots. Earlier, an ATX board used to have 5 or 6 PCI slots and a uATX 3 PCI slots. These days, it's usually 2 PCI slots for the uATX and 4 for the ATX, but these are not fixed standards.
Since a uATX has fewer expansion slots, manufacturers usually include a lot of onboard features such as graphics (IGP), network interface, sound, IEEE1394 (Firewire), etc. Some do not have a graphics card slot (AGP/PCI-E). A full ATX board, having more slots, may not have some of these onboard devices. But again, there is no fixed standard as to what is included on either board.
There is no fundamental reason why you should choose one or the other for gaming. Choose one that has the features you need.