I agree that its what he should be remembered for but most people under the age of 20 are more likely to think of him as Tony Montana. Even ask JGeoff, he said in his interview about The Godfather that he first started to love Pacino's work was in Scarface. Maybe he thinks Pacino did an even better job in The Godfather, but he was still introduced to Pacino by seeing Scarface.
Most people who were not alive when Scarface or The Godfather came out are more likely to see Scarface first because it is more recent and more appealing to the young age group. Therefore, younger people are more likely to remmeber him as Tony Montana.