The informal and polite form, 고마워 is used between close friends who is the same age as you, on the other hand, the formal and polite form, 고맙습니다 is used for strangers, people who you know and older than you like your parents, your teachers, boss, etc. We'v got more than 5 different speech styles depending on politeness and formality. You can get lots of details at ... http://en.wikipedia.org/wiki/Korean_speech_levels \^o^/

감사합니다 is the standard. When in doubt, just use that.