In my experience, Falcon matchups come down to speed more than anything else. Not frame speed, but movement speed. Falcon has a few unique attributes that give him some of the best maneuverability in the game which is a huge advantage over slower moving characters. But when he doesn't have the speed advantage, the balance shifts dramatically.
I've heard it said that Falcon is the "gatekeeper" of the high tiers, and I like that analogy. Falcon matches up really well with most of the roster below him because the lower tiers mostly consist of the slower characters in the game. On the other hand, Falcon struggles against most of the roster above him because most high tier characters can keep up with his movement.
Personally, I think the matchups make CF currently unviable as a competitive solo main. Most of the top tiers are either innately too fast (Sonic, ZSS, Sheik, Fox, etc.), or innately too small (Pikachu, MK, Diddy, Ness) for Falcon to be able to utilize his biggest strengths. Although he's fast enough to get in on characters like Ryu and Mario, the other top tiers pose too much of a threat and running into them in a tournament is still a huge risk.
That said, I think Falcon's movement gives him a lot of potential that we have yet to tap into. The discovery of frame cancelling could turn Falcon's dair into a viable approach option (even without frame cancelling I still think it's an underutilized move in neutral). New movement tech (like the moves in the Bidou tech video) could give Falcon better ways of maneuvering around projectiles and swords. We might get another balance patch. Who knows.
At the end of the day, Captain Falcon is just fast. He's really, really, really fast, y'all. And I think the way Smash 4 is played makes that a bigger advantage than ever. How Falcon fares in this game comes down to how well we learn to use his speed.