I have a lot of experience with Captain Falcon, so I'll make the best of it.
Captain Falcon is can obviously KO us with a majority of his moves, most notably Raptor Boost, back aerial, back throw, up aerial, or the Knee. And it's still kind of difficult to avoid getting combo'd by him even though Kirby's light. Also, Captain Falcon has better mobility and range to space Kirby out. And his edgeguarding can be brutal, solely on the high knockback of his tools, like his up tilt, both hitboxes of the down aerial, and back aerial. Aside from that, he can be juggled by Kirby's own up tilt, edgeguard him pretty well due to his average recovery, and Kirby can crouch under his jab, grab, and the late hit of his dash attack. The fact that he can duck under his grab is essential for spacing with Kirby and forces Falcon to use his other tools, which can still be potentially dangerous.
Kirby has to be careful when fighting Falcon due to his power. As mentioned, Kirby's crouch is his main approach, especially in this MU. You can utilize this by punishing whiffs like Kirby's down tilt, up tilt, or other moves depending on the attack Falcon misses. While Kirby has a good time edgeguarding him offstage, that doesn't mean you can be outright reckless anywhere. It is best to edgeguard offstage him when he is below the ledge and get as many ledge trumps as you can. Going offstage while Falcon is above the ledge could possibly result in getting meteor smashed by an aerial Raptor Boost, so it's best to wait onstage to see what his recovery option is and occasionally throw out some hitboxes. Besides edgeguarding, Kirby has a bad time KOing Falcon because of his fast falling speed and somewhat heavy properties, meaning that he can take a bit of punishment and use it effectively via Rage. That's not to say that all of Kirby's smash attacks can't KO for up to 150%, but Falcon can survive the knockback of them for up to around 100% at best. Kirby's Rage can boost this further for even earlier KOs.
In the long run, Kirby will be crouching for the most part, forcing Captain Falcon to mainly use his aerials as spacing tools. Kirby will try his best to push Captain Falcon offstage for gimps, while simultaneously racking up his percent to KO percents for his smash attacks. However, Captain Falcon can juggle Kirby and finish it with a Knee, land a hard-hitting back aerial, or meteor smash Kirby offstage. He just generally has more KO power and range than Kirby, giving the puffball a tough time to compete against that. I feel like it's 60:40 in Falcon's favor.