As I thought watching the first one, this sequel is a better movie in all respects: a better villain, with a better plot, and with better companions for Watson and Holmes.
In particular, I think this movie handles Holmes' sacrifice at the Falls perfectly. Using Holmes' calculated-combat trick here is sheer mastery: we get a physical climax which is reflective of the combatant’s mental sparring – especially when Moriarty gets into the act – and we still get the proper climax of Holmes throwing himself off the falls, legs wrapped around Moriarty, sacrificing himself for the greater good. The fact that we haven’t seen Holmes' calculated combat since the start of the movie lends this scene extra weight; we’ve been waiting for them to repeat the gimmick from the first movie, so this is a payoff on multiple levels.
Altogether I think Jared Harris makes a brilliant Moriarty, easily my favorite on film, and second only to the portrayal of Moriarty in tv’s Elementary. He’s threatening and clever and cultured, all at once, with a calm exterior that belies a rage bubbling up underneath. He’s not surrounded by stupid minions that have to be cursed every five minutes, he’s surrounded himself with other master criminals, all working to implement his well-thought-out schemes. I don’t think he raises his voice once in the movie, and yet everything he says feels like the important words of a powerful man.
As for the other rough edges from the first movie – the extended action sequences and Irene Adler – those have been polished out.
Adler’s death early on removes a weak actor while lending Holmes' character more depth and giving him – and therefore us – a personal stake in what had been, till then, a very abstract criminal plot.
The extended mass fight pieces have been entirely cut. We get one acrobatic sequence with Holmes, Madam Simza, and the Cossack, and then the flight sequence where everyone is fleeing the factory. But neither of these degenerate into the general face-punch-kick-ouch-hold-turn-kick tedium from the first movie. The flight sequence in particular is a fantastic use of slow-down effects and running the actors at a different speed from their surroundings to give us a good sense of what’s happening and convey some of the otherwordliness of being on the receiving end of an artillery barrage in that era.