As Echoes mentions, Coppi was the better cyclist of him and Bartali and he had a bigger influence on cycling. He was lightyears ahead of his times in regards to training, diet and mechanics.
His impact on the Italian society in the immidiate postwar era was - as in the case with Bartali - also great. Especially his victory in the 1946 Milano-Sanremo had a huge symbolic significance for the Italian people.
When he was later adopted by the Communists and promoted as a Communist hero, his impact on the society didn't decline. On the contrary, as the historian Simon Martin has argued,
"as important as Bartali’s immortalisation by the press was, it was the demonisation of his supposedly Communist rival Fausto Coppi that had arguably the greatest impact"
Additionally, his affair with la "dame bianca" and the subsequent trial even led to changes to the Italian civil Law.