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For English pleasure I would just pull the mane and have it short. Western events you either leave it long (speed events, cow and reining horses) or band it (halter and western pleasure) from what I've seen. I do believe some halter horses have long manes, but I think the banded mane shows their neck better.
I'd trim them and get them both even looking. Band for western, braid for english. Some breed shows do not trim the mane and let them be natural (Arabians). If you are doing a breed show, look into what the other riders do. I prefer a nicely groomed & braided/banded over a long uneven mane.
If it's a schooling or fun show, you don't need to braid, just make sure everything is neat and clean. If it's a bigger show, you should braid for the English class and you will need to pull the mane if it's long. I'm not familiar with requirements for Western classes.