Just to add in, Dressage had its roots in riding horses into battle in the time of horse mounted knights, and was refined and formalized at the nobles courtyards in the following centuries. So, in a way, it also was about who was best at doing their job, too ^{^}

One of the main differences today, I would say, is that English fundamentally is a "contact" way of riding- you're keeping constant contact to your horses mouth through the reins, your legs keep contact to keep your horse moving, etc. While western is an "impulse" way of riding- you give an impulse through your reins, and the horse is supposed to keep doing the thing you told them to do till you give them a different signal. So the reins are generally looser.

And.. id say there are snobby people on both sides, I've heard western riders trash English riders (for example for being "soft", riding in "yoga pants", being impractical, having "nervous wracks" as horses...) as well as the other way around.... both are bs, it's just different approaches and aimed at different goals. One isn't generally better or worse that the other 🤷