Well first of all, they're pretty well matched. Yoshi does better in the air, while IC's does better on the Ground, and have more versatile specials. Problem number one is that Yoshi is probably the best separating character against the IC's. Besides his obvious Egg Lay, His Ftilt, Bair, SideB, UpB Eggs, Ground DownB, Quick Discarding with Grabs, and even his Jab can also separate them easily. The main problem is that once Nana is in the air, Yoshi can very easily follow Nana with a 3 Hit Uair WoP for an easy kill with her relatively dumb AI, which in most cases you are unable to follow to save her.
Problem number Two is that Yoshi can gimp the IC's recovery so well, it's redicious. His Dair can cancel out your UpB. What makes it worse is that it desync's it, so if you panic, both you and Nana will do their UpB at the same time, but won't attach to eachother, Not to mention if you do take your time to readjust, Yoshi will have enough time to Edgehog, making you ditch Nana in most cases. It's the same if you're using your SideB. Dair also works, but Eggs are even worse. If you get hit by an egg when you're recovering with your SideB, it will cause you to scatter, and once again, cause a Desync, which will make Nana drop like a rock if you Panic and don't readjust. Course readjusting could also lead to an edgeguard If Yoshi follows up fast enough.
Course, they still have the legendary Infinite, but It's hard to snag an approaching Yoshi due to his fast horizontal speed, going past a shield grab if it happens. Plus a good Yoshi can deal with Nana easily, so you really won't have many chances doing such. Anyways, That's my view on it. I say about a 2 on your scale. We have 6:4 on ours, and I'm not going to lie, Infinites are scary, but he has so many ways to take out Nana, a good Yoshi usually doesn't need to worry about that.