Karlsson is farther along in terms of popularity and individual accomplishments at this point in his career than Alfredsson was. If Karlsson retires today, he's a HHOF considering every other player with his level of individual achievements have gotten in. Alfredsson with twice as long of a career is not in yet.
In terms of reputation, Alfredsson benefited from being in his prime when the Senators were a contender. Karlsson has played out his career thus far on playoff bubble teams. Alfredsson never carried the Senators in the way Karlsson did during last year's playoff run.
For me, Karlsson is above Alfredsson even now. But to the general public, I still think Alfredsson is #1. Look at how successful the Senators milking his number retirement was for them. Outside of a very short window, they did not sell individual game tickets, tickets to the game could only be purchased as part of a package deal with multiple other games, yet it still sold out.
I think Karlsson will easily overtake Alfredsson in terms of how he is viewed league wide by non-Senators fans, but locally I don't think it is a shoe in if he stays. Fans are very fickle, so if we fail to make an impact over the next 8 years, regardless of how wrong it is, I think that might prevent Karlsson from overtaking Alfredsson locally. If we have even a minimal amount of success, maybe one more deep run with our typical playoffs every other year, I think Karl passes Alfredsson if he plays out his career here.