Show me what you have = Show me what you posses/have in your possession. In this sense "got" is not needed.
Show me what you have got = Show me what you have received/acquired/obtained... You could extend the meaning of "what you have got" to "what you have got or received from God, or your parents, or what you have developed on your own" to mean your strength, guts, what have you. Thus "show me what you have got" can mean a challenge: show me your best move, show me what you are made of, as scrappy adolescents might say before a feast fight.