I'm guessing it was because Simba was alot higher up then Kovu, so the winds were mais higher up, so only affected Simba, or it was to make Simba look abit mais dominereing and make him look like he's got the most authority.
Because they were facing each other. Simba was facing in the direction where the wind blew against him, therefore making his mane blow. Kovu was facing the direction where the wind was blowing. Maybe it's the other way around.