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Both Characters Air Game Against Each Other:
Meta Knight hurts in the air. Like, a lot. He has range, speed, and very little lag; all we have going for us is the decent range of our F-Air for spacing, but even that can be relatively easily intercepted. B-Air is good for a quick "OMG GET AWAY" move if you're right on top of them, and U-Air can be used as a surprise move from below (most Meta Knights wouldn't think a Diddy would chase them in the air... but with good reason). D-Air will not hit. I'm almost 100% sure, unless you manage a Single Banana Lock or something. As for N-Air, well, his is the same thing only better and a kill move. Meta Knight can juggle you to no end with a flurry of U-Airs and Tornados and blow you to the side with a D-Air, and his F-Air and B-Air are quick damage dealers that aid a lot with gimping. Did I mention gimping? Oh yeah, Meta Knight is really good at gimping. You HAVE to mix up your recovery to hope to get back; as people have said, aiming for the stage and not the ledge with Up-B is a good idea, and some people like to Side-B AWAY from the stage and then Up-B back (so that the Meta Knight can't chase them as well). Overall, though... Good luck. Meta Knight's favor.
Both Characters Ground Game Against Each Other:
This is a mixed bag in my opinion. Diddy's Bananas are some of the most effective tools for punishing Meta Knight, but you have to be nearly perfect in your spacing and timing. If he perfect-sheilds and you try to chase, you'll eat a D-Smash before the Banana lands to trip him again. His Dash Attack is great at picking up Bananas, as are plenty of his other moves, and he has a Glide Toss that will cover most of the stage (which can be good or bad, really). His Dash Attack will also go through your shield, so learn how to punish when the foe is behind you. Our Dash Attack is a great way to rack up damage and start combos, but he can OoS Shuttle Loop through it or just Shield Grab if he has the timing down. If you manage to shield one of his D-Smashes, ROLL AWAY! He can D-Smash again before you can do just about anything. The name of the game against Meta Knight is to wait for him to use a mis-spaced move and then hit him with a Banana and go from there. If you are good at punishing, this can be in Diddy's favor.
Moves To Avoid and HOW to avoid them:
Tornado. You can throw a Banana to stop it, but he will likely just start another one again since the Banana won't make him trip (he's in the air). You can F-Tilt or Diddy Hump him out of it, but that takes INCREDIBLE spacing, which is all the more difficult due to the speed at which Meta can cover ground in the Tornado. Just about the only thing you can do if you can't follow up the Banana hits or are out of spacing range is to angle your shield and punish the after-lag, so you need to get used to telling if he'll land in front of, behind, or farther away from you after it's done.
U-Air. This move is avoided simply by not being above Meta Knight, though if you are, very well-timed Air Dodges can get you back to the ground (if they aren't baiting you in the first place). A Side-B can gain you some horizontal distance, which should help as well.
D-Smash. Just stay out of his range for this move, and if he gets close enough to use it, ROLL AWAY. You practically cannot punish this move if he's up close, so don't even try. Side-Stepping won't help much either; Shield and roll away.
N-Air and D-Air. These will be the moves gimping you off the side of the stage; just remember that the sword, as disjointed as it is, is still attached to Meta Knight, so if you avoid Meta's body as you are recovering you'll have an easier time of getting back.
Diddy's Moves to Utilize In The Matchup:
Bananas. Bananas help you punish his moves and keep him from landing where he wants to land. They'll stop sliding Grabs and Dash Attacks if they are behind you, and they'll limit approaching options if they are in front of you. Banana control is VITAL to have a chance in this match. Always have one out; if you don't have one, knock them away with a decent knockback move or with a grab and pull one immediately. Just pulling one randomly will get you punished by his speed.
Personal Strategies To Help With Matchup:
Camp, to a degree. Use Peanuts and Bananas to bring Meta Knight back to the ground and proceed with the beatings form there. Wait for him to miss an attack, and then punish as fast as you can. Once you're out of range to hit with another move in a combo, RUN AWAY. Meta Knight will just punish you if you try to chase him without a Banana.
Stay in the middle of the stage. I can't begin to describe how vital it is that you don't get knocked off the side. It's almost worse to recover against a good Meta Knight than it is a good Marth.
Overall Character Ratio:
I'm on the side for 60:40 Meta Knight; if you're off the stage, that's a stock. His D-Smash will blow you out there too quickly, and from there it's almost a game of luck getting back. Your ground game rivals his, though, if you can control your Bananas; just make sure you're on a flat stage or you're in trouble.
Please correct me if I'm wrong about any of this, or if I don't know something I should. This is all from my experience, which isn't terribly much.