This is how I look at it:
Pros
-Capt. Falcon dominates Diddy Kong in the air
-Diddy Kong('s recovery) is easily gimpable off-stage, whether with U-Airs or flubbed F-Airs
-Grabs work pretty well against Diddy Kong
-Raptor Boost punishes most errors, allowing for a versatile branch of attacks
-N-Air disrupts Diddy Kong pretty nicely
-SHAD helps to position yourself better
Cons
-Diddy Kong dominates the ground; bananas just overall overwhelm Capt. Falcon (huge pro for Diddy Kong)
-Capt. Falcon is heavy, making it easier for Diddy Kong to set up for more attacks
-Diddy Kong spikes rather easily
-Diddy Kong edgehogs fairly well
Disclosure: Overall, just a matchup you REALLY want to avoid. As mentioned before, Diddy Kong's ground game overwhelms Capt. Falcon, making it rather hard to approach with many attacks. Falcon Kick is pretty much futile against a Diddy Kong, simply because you'll most likely run into a banana, which allows Diddy Kong to punish very easily. As far as edgehogging, Diddy Kong does a fairly good job at it. His D-Tilt is pretty spammable, so watch out for it. From there, he can either just grab the edge, or even just B-Air you against the stage at higher percentages, or just spike you. It really depends on the player you're facing. I prefer not to use B-Airs, simply because Diddy Kong is a small character, so the chance of hitting him is pretty iffy.
However, Capt. Falcon does outdo him in some aerials. For one, the air. Out of your aerials, SH N-Airs help a bit in disrupting him. U-Airs and (flubbed) F-Airs help for gimping, even tripping.AC D-Airs help to set up for more aerials. Diddy Kong's bananas can easily backfire on him, but in the hands of a good Diddy Kong player, this is subject to change. Dash Attack and Raptor Boost are good ways to TC him, which easily flow into U-Airs. As for throws, D/U-Throws are good, as they lead into more aerials. F-Throw is tolerable at low percentages, but I still prefer to use D/U-Throw.
Overall, I'd say 35:65, Diddy Kong's favor.