As nibbler said;
Mini ITX is the ‘proper’ name, I and others say
ITX for short.
I’d expect an AM3+ or any other desktop CPU socket ITX board to consume as much or slightly less power as an equivalent ATX board; it features pretty much the same hardware but the board is physically smaller with fewer DIMM and PCI(e) slots. These ITX boards which are smaller versions of larger boards are becoming increasingly common, at least with the Intel platform.
The most common form of ITX board features an onboard processor, it’s simply a CPU soldered on to a motherboard, these CPUs and their accompanying chipsets tend to be low powered e.g. Intel Atom or ‘mobile’ parts, hence low power consumption but performance suffers, they’re not great for gaming.
Most people go for mini ITX for its small size, for example my next gaming rig will be crammed inside the
Silverstone SG06 which takes ITX boards (build log to come next week!)
I decided to go the Intel route because there are currently very few AM3 and no AM3+ ITX boards available.