Falco... He has a terrible jab. The only good qualities it has are its low startup of 2 and that both jab 1 and jab 2 cover entirely in front of him since jab 1 is an overcut while jab 2 is an undercut allowing Falco to anti-air with his jab 1 as said before. It can also be ledge canceled: https://www.youtube.com/watch?v=K1gk1M4ubnk
, which is great since Falco can weirdly confirm a Nair from it, but it's so situational and definitely not enough to make up for all its problems. Everything about his jab after that is just terrible. For whatever reason, Falco's jab has unusually high recovery shared with Peach who also has a frame 2 jab. Most normals have 20 to 30 recovery frames, lower for moves like tilts, higher for moves like Smashes, and in between for moves like aerials and dash attacks. Specials being special, they're different. For jabs, most of them have recovery below 20 like between 14 and 17. Falco's jab 1 has 19 recovery frames, jab 2 has 21 recovery frames, and rapid jab finisher has 34 recovery frames. For Peach, we're talking about 25 for jab 1 and 27 for jab 2. Here's the thing, though, Peach's jab 2 / jab finisher will always reliably connect, so Peach not having the option to go for jab mixups isn't really a bad thing then she can frame 2, slap your filthy ass away from her princess self. Falco doesn't have that luxury.
In Brawl, Falco was known for his jab mixups as jab had 11 recovery frames and jab 2 had 13 recovery frames. Both also had set knockback, 5 for jab 1, so not really that useful even with it doing 4%, and 20 for jab 2. Here's the thing, it wasn't that abusive compared to Smash 4 Fox's pre-patch jab or even Link's pseudo-jab infinite. Why? I don't really know, but I can only guess that because of Falco's higher hit angles compared to Fox's. Anyway, despite it having really low recovery, Falco couldn't really jab lock like Fox, but it did give him a really good jab mixup. Speaking of which, the times where Falco, Brawl or Smash 4, does jab 1, jab 2, jab 1, and repeats and you see a someone, a random player, getting caught in it, then they're not DI'ing at all. Just push out, geez. Then again, there are people (on For Glory) who will DI in during a rapid jab for whatever reason. Genius! Let's take +30% from a jab because you somehow think DI'ing into it would do... what the hell do you think would happen? Why!?
In Smash 4, jab 1's damage was dropped to 3%, jab 1 and jab 2 have regular, but low knockback, and their recovery wasn't just upped to make it so Falco couldn't abuse it, but increased to the point where jab mixups are risky. In a way, it got the Blaster treatment of making it so Falco couldn't just abuse it, but using it in the first place is risky even at max range. So, if you can't jab mixup, then go for a full jab, right? Yeah... about that. Falco's rapid jab, for whatever reason is weird compared to other jabs in how it transitions. For almost all characters, you can hold down attack and they will go through their entire jab combo without much of a problem. This is helpful for characters with both a rapid jab and a jab 3 which in their case, will do a jab 3 if attack is held down except for Little Mac who does rapid jab -- he's the only character who has a "reversed" input outcome. The other option, of course, is to just tap and mash it and that's just fine too. For Falco, he's the only character who has a different transition depending on if you hold or mash attack. If you hold attack, there's a delay between jab 2 and rapid jab that characters with frame 3 and maybe frame 6 moves, especially if they have armor or are invincible, can hit him during the transition. Otherwise, most characters can jump out from floaties like Kirby to fast fallers like Little Mac. If you mash, then there's less delay between jab 2 and rapid jab. It might be a minor thing, but it can be weird for players who switch around e.g. just casual play and friendlies where you didn't know and you keep getting hit out of jab for some reason as Falco.
Now, rapid jab itself and rapid jab finisher have issues with connecting. Rapid jab, I don't know what the problem is, but you can easily jump out of it by moving out. It doesn't help that it actively pushes people out unlike some rapid jabs that seem to pull you in or push you up or around. Falco's rapid jab just pushes people out to the point where even the 4 minimum hits can push you out far enough that you have time to avoid its finisher. Often, Falco will be stuck in rapid jab with his opponent out because rapid jab pushed them out too far. At that point, it's a guessing game where Falco has to decide between holding rapid jab hoping his opponent runs into him or he lets go and the finisher can catch his opponent which if he misses, 34 recovery frames to deal with. For shorter characters, they can even land during the transition and end up below the hitbox of rapid jab. As those characters have smaller hurtboxes in the first place, mashing jab to get the quickest transition isn't ideal as Falco would be connecting rapid jab while they're very high up and able to just jump up and away.
The only thing I know between Brawl and Smash 4 is that rapid jab's damage was decreased from 1% to 0.4% and that between Brawl and launch Smash 4, its transition frame was upped from 7 frames to 9 frames. 1.0.8 dropped it down to 8 frames which doesn't really do much? Just 1 frame and if that's the frame where you mash jab, it probably didn't do anything to make it connect better in that case. Everything else about it is unknown like most rapid jabs. Brawl's, I was able to find by digging through Brawl Falco's file and what I got was that it did 1% per hit, it has hit angles of 30, 50, and 80 degrees, and its knockback is 0 base, 3 set, and 100 growth. In hit frames dug through Brawl Falco's frame data thread and a Brawl Japanese wiki, startup of 2, 1 active frame, and 4 frame gaps between each hit. Smash 4, I was able to at least get its hit frames and it's the same except for the frame gap which is 5. A drop in 0.4% shouldn't be that much loss in hit stun if it has the same knockback... I bet its hit angles where changed, but I don't know because nobody bothers to find rapid jab data.
For rapid jab finisher. The move itself is fine with the only problem being outside of its high recovery, is that out of the rapid jab finishers, it has one of the lowest overall knockback and I don't know why. Other rapid jab finishers have good base and ~130 growth while doing anywhere from 2% to 5%, but Falco's only does 3%, 60 base, and 100 growth which for a low damage finisher and basically a "multi-hit finisher", should have growth in the 130's and not the 100's unless there's a reason like Captain Falcon's rapid jab finisher has insanely high base, 110, but lower growth, 70. That being said, it's not limited to just Falco as Mewtwo's rapid jab finisher has low overall knockback too as Mewtwo's rapid jab finisher does 2%, 82 base, and 100 growth, but Mewtwo's jab in general is miles better than Falco's. Anyway, what Falco's rapid jab finisher is attached to ruins anything good about it. Because of rapid jab's issues, rapid jab finisher doesn't link well and there's nothing you can do about it like with his jab 2 to rapid jab where you can vary or the timing.
Between the high recovery of jab 1 and jab 2 and the delay of jab 2 to rapid jab and rapid jab to rapid jab finisher, characters like Jigglypuff, Little Mac, Luigi, Ryu, Roy, Yoshi, and characters with fast, strong, and protected -- armor or invinciblity -- moves they can outright KO Falco because he jabbed them effectively making jab a hit confirm for them. For other characters like Lucina, Mario, and Marth, he's going to take damage and usually more in a terrible trade. At lower percents, some characters can even jab back at or grab Falco if he hesitates during jab 1 and jab 2. Otherwise, like I said, pretty much anyone can just jump out.
So, Falco's jab is a Morton's Fork where whatever choice you choose, it's just as bad if not worse. Each part can be considered a series of unfortunate events.
1. Falco hits with jab 1: if he stops, he has too high of a recovery on it for a mixup to be safe, but if he continues he has to commit to jab 2.
2. Falco connects with jab 2: if he stops, even higher recovery than jab 1, but lower damage and lower knockback making it even less safe for a mixup. If he doesn't stop, then he has to commit to rapid jab which in this case, if he hesitated or paused, he could have already screwed himself before jab 2 ends or rapid jab has to start.
3. Falco hits with rapid jab: hope that his opponent didn't jump out already or the damn thing didn't pushed them out already. If they did, then it's hoping his opponent is in front of him and the finisher can catch them... If they're behind him or have a weapon, welp... RIP.
It's F-tier to the point where I would argue that if Lucario's jab, as bad as it may be, can reliably connect, then Lucario's jab should be in D-tier and Falco's should be in F-tier by itself.