Trying to catch up to melee is hard, but hopefully not impossible. It will take a good amount of good, consistent practice. I know this because I have played quite a bit of melee inconsistently (on and off, with months in between periods of playing) and badly (practicing the wrong things, getting set in bad habits, and not thinking while I play). A couple of my friends and I started playing again this summer for the last two months. I may not be that good of a player, but here's what I've learned if any Brawl players are interested in trying to learn Melee:
To learn to play, you need to know what you're weakest in. I've often practiced the wrong thing or neglected another completely. There are 3 parts to Melee:
Tech skill - the physical ability to use a character's moves and skills. Ranging from being able to preform a simple uptilt to being able to waveshine someone. Spacing is also a tech skill IMO.
Strategy - reading your opponent and their character. It is a very general idea you are trying to implement. For example, you're playing a marth using sheik and your stategy is to play defensively. Or maybe you're playing as jiggs and want to camp a lot during the match. Or maybe you're playing marth against a falcon, and you decide you want to stay close against him on the ground, so he can't fair as easily. You can learn plenty of strategies here on each character's smashboards about match-ups. How you mix up your approaches is another example of strategy.
Tactics - what to do in specific situations. For example, you're marth and you upthrow a falco at a low percent. Your tactic in this situation is to: if he DI's behind you, you uptilt. if he DI's in front of you, you regrab him. if he DI's away, you forward smash or chase him. Another example, you're playing fox with marth at a middlish percentage, and he upthrows you. You know he'll probably try to hit you with an upair right after, so you know to DI away and through out a Fair as quickly as possible to stop him.
Tactics are the most important part of the game I believe. Tech skill and strategy can open up better tactics for you. They give you the ability to combo and defend/avoid. Practicing tactics requires you to have another person to play with and thinking about what you're doing and why. After a while, you can create good, habitual tactics. It's hard to react fast in situations and come up with what to do every time. Even watching videos only allows you to see what happens in one case. You might see a good Marth player upthrow someone and then uptilt, but you didn't learn what to do if the other player DI'd a different way. Or if they were at a different percentage. Or even if the stage was different and there was a platform above them.
Anyway, those are the parts I've been working on while playing with a few of my friends over the last couple of months and I've seen a decent bit of progress. These all may seem obvious and very general, but it's suprising how often one area will be neglected and how disorganized a person's praticing will end up. Yeah, anyway, Good luck playing! It is hard, but who cares as long as you're enjoying it.