Both Characters Air Game Against Each Other:
Airgame on stage is about even. As said, each character can punish each other equally and trade hits. Diddy has a slightly easier time juggling ROB, while ROB can land harder hits in the air easier. The air game is solely ruled by player skill and outperforming. Each character has a range attack in the air that can set up strings, with ROBs being more difficult but more powerful with Diddy's being vice versa. Offstage, ROB performs better. A great recovery allowing plenty of counters to any gimps Diddy may try, as well as being able to travel offstage after Diddy without (much) fear.
Both Characters Ground Game Against Each Other:
The ground is a different story from the air sadly, with ROB having enough camp and punish that tips the matchup in his favor. Diddy can't sit behind bananas all day due to ROBs projectiles, as well as can't throw his bananas around too much for fear of ROB nabbing one. If ROB gets a banana, things can become quite annoying and it becomes priority to get it away from him. This is where ROBs camp and punish shines the best, with three (Or four if that second banana got away too!) projectiles and glide toss setups making you sure to be in fear.
Moves To Avoid and HOW to avoid them:
Don't bother trying to pick up the gyro, it's just going to make you mad. You'll not only take hits from it randomly, but you'll also open yourself up to punish by taking the bait. Just as Diddy can punish when characters go for his bananas, ROB also excels at this. Attempt to put yourself between the gyro and ROB so the wall stops existing for the time being. This also removes a key move from ROB momentarily, making it an excellent chance to move in (Don't forget to shield that incoming laser though!). Other moves to watch out for are all of his kill moves (Nair, dair, bair are deadly when being air dodge baited) which will destroy you at early percentages, as well as dsmash. This move is annoying, keep your distance.
Diddy's Moves to Utilize In The Matchup:
SideB is great against ROB as has been said. You'll want to throw this in, but don't finish the flip with a kick very often. It's high risk low reward, the extra possible damage is not worth the incredible punishment ROB can lay on you. Bait ROB with bananas if you feel confident about it. Throw one near him and capitalize when he goes for it with sideB or even better; a rising Fair. This is especially recommended since ROB is large and leans forward when on the move. ROB is quite big horizontally, so if you're next to him do not be afraid to dribble right through him and almost always land a trip. Bair out of shield works well against ROB as well, mostly because if a ROB hits your shield there is a high chance they're going to spam Dsmash which you will be hopping over and punishing with.
Personal Strategies To Help With Matchup:
Be good. This matchup is tilted almost entirely by player skill. If you want to win this, you have to know the matchup better than your opponent. If you end up winning game one, it's not over yet. ROB is at a much larger advantage in a good counter pick like Frigate or another ROB favored map such as Halberd. It will likely go to game three if player skill is equal. If you lose game one though (Which on a conservative stagelist, you shouldn't), you're in a largely uphill battle.
Overall Character Ratio:
ROB 55-45
Quick summary: The matchup is even in almost all areas. Sadly, almost exists in that sentence. ROB will win on more stages than Diddy will, has a great ground and offstage game, and will punish and kill early. However, Diddy's usual tricks still can slip up ROB provided a proper environment and will rack up damage due to ROBs size/speed and general predictability.
Note: I've played this matchup quite a bit, but not against any pro ROBs yet, so my input may be inadequate.