I just watched a ton of highlight videos from him and I think that the ability to draft him also helped to seal Hall's fate. I don't see Hall being able to do any one thing better than Puljujarvi with the exception of top end straight away speed and Puljujarvi is far from a slow guy himself.
I'd say that Puljujarvi has better hands, a better shot in terms of wrist and slap shots (at least accuracy wise), is bigger and more physical, plays away from the puck better and while it's too early for me to say for sure, he may think the game better as well (his play away from the puck points to this IMO). Naturally I don't expect him to replace Hall this season as that'd be unfair to any non generational 18 year old, but in 1-2 years time this guy should be a high end offensive player at this level.
Both have good onetimers although since Hall carries the puck so much at ES he only really uses them on the PP when he's on the half wall and the puck is moved around a bit more and there's more space out there.
I'm not sure if Puljujarvi tops Hall's best season production wise or not but I think that he will be a better player for us on a better team than Hall ever got to play on in the NHL and his skill set should gel with McDavid more than Hall's did.
I also wonder if we might see Jesse on the point on the first PP unit because he has a good clapper and one timer across form McDavid?