If the character on the right sounds un-ironically appealing to you, then you either 1) Haven't dealt with very stupid Author insertion Mary-Sues (Or Gary Stus, for the men) before, or 2) are one. In the latter case, I hate you.

Listen, I get it, you want escapism, you want fantasy, you want a character who is above all the world's problems, and if that's what you want to create, fine. But here is the thing, these characters, aside from being just pure imagination masturbation, are REALLY BORING. They never have any character flaws and usually eschew any personality or deep insight for being 'cool' or 'cliche.' They never experience any character growth and can always overcome every challenge with a snap of their fingers and that is BORING. Other people don't want to hear about your boring ass self-insertion porn. EVER.

Based on a person who I actually knew who had an avatar like this, who she talked about as if she was real. Incessantly.

*BTW, I don't see this as a gender issue. I happened to address a female character here, but I've seen just as many examples with men, so don't think I'm chauvinistic.