Road shoes are lighter and can be used with road pedals and some have the two hole pattern for mountain bike pedals. They're usually stiff soled shoes and make it harder to walk around in.
Mountain bike shoes are more versatile off the bike. Obviously you can walk around, however you may be limited to mountain type pedals. Mountain bikes are usually heavier and may not be as stiff as road shoes. However, shoes are so stiff now, they won't make much of a difference.