In a nutshell
Captain Falcon is arguably the melee veteran that was most negatively impacted by Brawl's physic change, and he received some nerfs that affects his performance really badly as less hitstun and the loss of L-canceling result in drastically fewer, weaker combos, and a less effective dashdance and inability to moonwalk give him even fewer options. Captain Falcon possesses both fast speed and strong attacks. His has low traction, but makes it up with having the shortest tripping animation. Falcon mainly needs to play a hit-and-run style, and his speed helps him greatly in this playstyle. Captain Falcon can rush in to punish any mistake and flee. He can play a decent air game, having good aerials like the knee which can be powerful when sweetspotted. Falcon's aerials tend to have poor hitboxes, making safe approaches nearly impossible, especially when considering his lack of projectiles. The Captain's small hitboxes and no disjointed hitboxes which gives him difficulty approaching or breaking through a camping character's defenses. Captain Falcon is currently ranked 34th (G tier) on the tier list as the overall result of all the above.