The matchup is mostly about falcon trying to force luigi into the air. Falcon's grab can actually do something to luigi, but not the other way around, unless you get a tech chase at a reasonable percent, where you won't get CC'd by falcon's amazing weight. Though falcon can't really do a legit combo from a throw, falcon's u-air ***** luigi once he's forced in the air. He falls slow and has no air mobility, so falcon walks all over him when luigi is in the air, with some generic combos, that will either force luigi offstage, or you will hit him with a knee and he will die. Falcon can also force luigi into the air with his amazing n-air. D-air / knee also are good, but harder to hit. Falco's knee at mid percents, can potentially kill luigi, because his recovery sucks so much ***.
They are both incredibly fast on the ground, but luigi's problem is that to keep up, he has to commit to a wavedash, which takes about 10 frames to be active (after the jump). There's a lot of openings, considering that falcon can cover the whole stage so quickly.
The both get ***** on edgeguarding, but luigi can get random misfires that will save periodically. Once luigi wastes his jump, falcon can literally jump at him and d-air. Then if luigi meteor cancels, it doesn't matter, because he goes straight up.
I don't think the matchup is that bad, but not close.
Edit: luigi also has some good combos on falcon, but he's never going to death combo him, unless he west coast DIs, or gets tech chased -> up-b at like 100%. If you combo falcon off the stage, because of his amazing weight, he won't go that far even at high percent and will most likely recover.
That's some info that I have. I would post more details, but I have to go home now.