Raziek
Charging Limit All Day
Ok, so here to offer my input. I'll go back and do Sheik later, as I promised that and never delivered.
I think anywhere between a slight advantage and a slight disadvantage is reasonable for this matchup. I lean towards even, with us having much more flexible stage counterpicks than he does.
Both characters have a really strong advantage time in this matchup. Falcon is an easy-to-combo weight and size, has a really hard time dealing with Arcfire/Speed Thunder/Elthunder, and is horribly vulnerable to Nair/Elwind gimps (offstage) and Uair/Grab traps (onstage) Conversely, Robin has a similarly difficult time getting down once Falcon gets her off the ground, but I don't think he has it as bad as he does. Her main weakness is lack of tools to defend herself while recovering (using Elwind).
Neutral Game
So, Falcon has a few main tools in the neutral game. His crazy range dash grab, his ridiculously quick dash speed, and his disjointed dash attack. Other than that, he really doesn't have much to play neutral with. His jump-ins all lose free to SH Fair/Uair from Robin. His general goal is to get in, land a grab/jab and convert that into a Uair juggle and eventual edge-guarding situation. At that point, he's then looking to close out the stock on the edge-guard. I find probably 80% of my deaths to Falcon are to his Bair offstage.
We have a pretty clear gameplan, though it varies by stage. Our main goal is to force him to have to jump when he's approaching us. As @Trifroze already noted, Falcon's dash start-up is actually pretty long, and his walk is awful, so we can actually react to his dash simply by throwing things at it. If customs are legal, Speed Thunder and Speed Elthunder are hell for Falcon to try to dash at, and are extremely safe. Otherwise, regular Elthunder and Arcfire fill this role pretty well. He also correctly noted that Arcfire should always be retreated in order to prevent punishment. Ideally, Robin is throwing it with platform cover above and in front of her.
The horizontal spacing game is designed to either rack up damage a little bit at a time, or convert into positioning/edge-guard by landing Arcfire. Falcon's model is wide and his shield size means if he tries to shield Arcfire, he is frequently stuck in the middle of the hitbox due to how far he slides during his dash. He really has to respect it, since it's not something he can just powershield and ignore.
Once he gets into boxing range, SH Fair and Jab are our go-tos. The Wind jab buff helped this matchup a TON, as Falcon has an extremely hard time getting out of it due to his fall speed. Otherwise, main boxing tools are D-tilt, F-tilt and retreating pivot grab.
Once Falcon's in the air, we can just abuse our disjoint. Falcon's Nair is insufficient for combating anything below and in front of him, so Fair just absolutely ruins his day. Once he's above us, he really has no answer to the Uair if we're spacing properly. His Dair lacks sufficient disjoint to beat out Uair, and you can trap his airdodge and grab him if he tries to airdodge past us into the ground.
I did some rudimentary testing of Ledge Eject setups vs. Falcon with @DaBeast just now. We don't have anything guaranteed, but if Falcon jumps he can get caught by Trump -> Sour Uair into Elwind or Trump -> Bair. It's a mixup at best however. I would stick mainly to Nair gimps, Fair, and Elwind spikes (or stagespikes) and/or harassment for the most part.
Once Falcon gets US off the ground there's not a whooooole lot we can do about the Wheel of Fortune (Uair chains). As was said, just take the damage and try not to eat Knee/Dair from air-dodging. At higher percents when they're not longer guaranteed, we can Elwind on reaction and land safely. I'm preeeeety sure we can't do much to avoid his Trump -> Bair, but I have not tested it extensively.
Other things worth mentioning: Falcon hates having platforms in his way in the neutral game, so I would try to stick to stages that don't just let him run around freely. (Avoid FD)
Nosferatu is also fantastic against Falcon when he's been forced onto a platform. His out-of-shield game is pretty bad, so he's pretty free to the (Robin jumps up from below you: Is it Nos or Uair?) mixup.
I might add more later, but I think that covers most things worth talking about. I think it's a pretty close matchup. Both characters have really exploitable traits, so it really comes down to which player is winning the neutral game more frequently. I think both characters have solid tools to do so. I do think it is likely a slight disadvantage without access to Speed Thunder, however.
I think anywhere between a slight advantage and a slight disadvantage is reasonable for this matchup. I lean towards even, with us having much more flexible stage counterpicks than he does.
Both characters have a really strong advantage time in this matchup. Falcon is an easy-to-combo weight and size, has a really hard time dealing with Arcfire/Speed Thunder/Elthunder, and is horribly vulnerable to Nair/Elwind gimps (offstage) and Uair/Grab traps (onstage) Conversely, Robin has a similarly difficult time getting down once Falcon gets her off the ground, but I don't think he has it as bad as he does. Her main weakness is lack of tools to defend herself while recovering (using Elwind).
Neutral Game
So, Falcon has a few main tools in the neutral game. His crazy range dash grab, his ridiculously quick dash speed, and his disjointed dash attack. Other than that, he really doesn't have much to play neutral with. His jump-ins all lose free to SH Fair/Uair from Robin. His general goal is to get in, land a grab/jab and convert that into a Uair juggle and eventual edge-guarding situation. At that point, he's then looking to close out the stock on the edge-guard. I find probably 80% of my deaths to Falcon are to his Bair offstage.
We have a pretty clear gameplan, though it varies by stage. Our main goal is to force him to have to jump when he's approaching us. As @Trifroze already noted, Falcon's dash start-up is actually pretty long, and his walk is awful, so we can actually react to his dash simply by throwing things at it. If customs are legal, Speed Thunder and Speed Elthunder are hell for Falcon to try to dash at, and are extremely safe. Otherwise, regular Elthunder and Arcfire fill this role pretty well. He also correctly noted that Arcfire should always be retreated in order to prevent punishment. Ideally, Robin is throwing it with platform cover above and in front of her.
The horizontal spacing game is designed to either rack up damage a little bit at a time, or convert into positioning/edge-guard by landing Arcfire. Falcon's model is wide and his shield size means if he tries to shield Arcfire, he is frequently stuck in the middle of the hitbox due to how far he slides during his dash. He really has to respect it, since it's not something he can just powershield and ignore.
Once he gets into boxing range, SH Fair and Jab are our go-tos. The Wind jab buff helped this matchup a TON, as Falcon has an extremely hard time getting out of it due to his fall speed. Otherwise, main boxing tools are D-tilt, F-tilt and retreating pivot grab.
Once Falcon's in the air, we can just abuse our disjoint. Falcon's Nair is insufficient for combating anything below and in front of him, so Fair just absolutely ruins his day. Once he's above us, he really has no answer to the Uair if we're spacing properly. His Dair lacks sufficient disjoint to beat out Uair, and you can trap his airdodge and grab him if he tries to airdodge past us into the ground.
I did some rudimentary testing of Ledge Eject setups vs. Falcon with @DaBeast just now. We don't have anything guaranteed, but if Falcon jumps he can get caught by Trump -> Sour Uair into Elwind or Trump -> Bair. It's a mixup at best however. I would stick mainly to Nair gimps, Fair, and Elwind spikes (or stagespikes) and/or harassment for the most part.
Once Falcon gets US off the ground there's not a whooooole lot we can do about the Wheel of Fortune (Uair chains). As was said, just take the damage and try not to eat Knee/Dair from air-dodging. At higher percents when they're not longer guaranteed, we can Elwind on reaction and land safely. I'm preeeeety sure we can't do much to avoid his Trump -> Bair, but I have not tested it extensively.
Other things worth mentioning: Falcon hates having platforms in his way in the neutral game, so I would try to stick to stages that don't just let him run around freely. (Avoid FD)
Nosferatu is also fantastic against Falcon when he's been forced onto a platform. His out-of-shield game is pretty bad, so he's pretty free to the (Robin jumps up from below you: Is it Nos or Uair?) mixup.
I might add more later, but I think that covers most things worth talking about. I think it's a pretty close matchup. Both characters have really exploitable traits, so it really comes down to which player is winning the neutral game more frequently. I think both characters have solid tools to do so. I do think it is likely a slight disadvantage without access to Speed Thunder, however.