In ancient Greek texts Achilles' status is that of a heros, a powerful human being who can accomplish great feats beyond the reach of ordinary people. Although he is entirely mortal, he's very very hard to kill (eventually this has to be accomplished through trickery) and he is unnaturally strong.

Asclepius is portrayed differently. So no, he is not similar to Achilles in stature.

One more thing about Achilles before you move on: Like Asclepius, he seems to have had some healing skills imparted to him by Chiron. In Iliad Book 11, Eurypylus the King of Thessaly asks Achilles' friend Patroclus to help him heal a wound: "spread the soothing, healing salves across it,/the powerful drugs they say you learned from Achilles/and Chiron the most humane of Centaurs taught your friend" (transl. Robert Fagles).

Admittedly, this turn to Achilles for help might have been because Asclepius's son, Machaon, had been injured by an arrow in the same battle and was temporarily unavailable. In Book 4 Machaon is seen in action as a healer, "deftly appl[ying] the healing salves that Chiron, friend of Asclepius, gave his father long ago."

Ironically, Machaon himself is eventually killed in the war by another Eurypylus, a soldier fighting on the Trojan side.