I am sorry, but looks or to be more precise, face, is far far far far far far far more important than any other physical trait. Only thing is that with face, you can't measure beauty... It's all about taste (although there are those who are ugly by all opinions and handsome by all opinions).
And no... a 6'3 does not win against a 5'10 guy.
Also, this "all else being equal" is stupid. Equality of looks does not exist between to seperate people. btw, to your same logic, a 6'1 could also say that he loses against a 6'3... Taller is not always better... Especially when you go above 6'... I come from a country where the average is 5'10... I have a friend who is 6'3 and also pretty ugly. But he curses each his height each time he is being rejected for being too tall (and he gets that alot).
I saw a post of yours where you are still in the "growing" age... You are young so therefore you are thinking in a very black and white way. Once you will grow up you will see that at 5'10 you are more than tall enough to get any girl there is out there... And sorry, but if you dont have any success with women being 5'10 the problem is not your height. You are either very ugly or have a really dull or non attractive character. I hope for you it's the second option since it can be adressed and improved