What is the difference between ATX and micro ATX motherboard or in others?
Which is better?
If cost is not a problem which I should buy?
The only real difference is size and shape, and by extension the number of PCI and PCI Express slots that are available. The form factor does not govern the number of expansion slots on a board though, so be careful and read the spec sheet for any board you are considering, as a cheap manufacturer of a full ATX board might give you the exact same amount of slots as a cheaper mATX.
You should buy one that fits your need, budget and -most importantly- case.
The typical microATX board has either 4 PCI slots or (3 PCI slots and an AGP slot). The typical ATX board adds another two slots. An older ATX or even mATX board may have an ISA slot or two rather than some of the PCI slots. Depending on the model, both types of boards may have either ob-board video or an AGP slot or both. Either type of board may have up to 6 USB ports, if you count the usual pair connected via a cable to the front of the case. Parallel, one or two serial, and PS/2-style keyboard and mouse connectors are almost always present on both types.
A micro ATX board will fit in a full ATX case. An ATX board will not fit in a microATX case. Duh! They have the same mounting screw pattern. A microATX board looks absolutely tiny in a full ATX case, but it does the job when you need a system with a lot of drive bays