Dr. Mario in a serious battle. He's just way more adaptable. Sure link has lots of projectiles, but its a little more awkward to smash with him in comparison to doc. Doc can hit hard any direction, while link is limited to few. So 1, Doc is faster timing wise on the attacks.
2) Dr. Mario has a lot more counters,
3) Dr. Mario has a lot fast grab then link making him more flexible.
4) His recovery is far faster than links, allowing him to counter more quickly. In example, his up B is a simple Doon, and he's done. Young link is like HAAAAAAAAAA!!!!, swirl swirl swirl.. within those swirls Doc can easily deliver a punch.
Basically young link is a lot more vulnerable then link, purely on attack recovery, throwing speed, balance, and the fact that he's easier to knock off teh stage than doc because the doc can take more dmg. That's probably another reason why doc is higher tier >.>