In AmE, "you got me" is usually used either A) as an admission that someone has guessed or surmised something obvious about you, or something completely implausible about you or the situation; or B) as an admission that you're completely stumped.
For example:
A) "It says here to press 'any key.' I can't find the 'any' key."
"I take it that you're unfamiliar with computers?"
"You got me. This is the first time I've touched one."
Husband: "I can't find my circular saw. Did you take it?"
Wife (sarcastically): "You got me. I was secretly adding a room on to the house and now you've ruined the surprise."
B) "Why do you think the boss has called for a special meeting this afternoon?"
"You've got me. Our sales were up last month, all the reports were filed on time....I can't think of anything that would be bad news."
"You caught me" implies that the person was in the act of doing something and was discovered by someone else:
Boss walks past Fred's desk during lunch hour and notices that Fred has a photo of a nude woman on his computer screen.
Fred sheepishly confesses: "You caught me. It's my friend's birthday, and I was making a funny card to send to him."