Self esteem is like empowerment to do something. You've got the "get up & go" and the "drive" or enthusiasm to do something. Ego has more a connotation of proud or boastful.
According to dictionaries:
Pride in oneself; self-respect; respect for or a favorable opinion of oneself
an inflated feeling of pride in your superiority to others; conceit;
I think some level of self-esteem is good, but ego really isn't. It's an inflated, over-done opinion of one's self.