The Kings are a dominant puck possession team. A focus on puck possession is one of the major changes that have come from hockey analytics.
We estimate possession primarily by looking at shot differential. It comes in many flavors -- Corsi or Fenwick, overall or score-close or score-adjusted. But for the last couple of years (since they acquired Jeff Carter, really), the Kings have topped every version of a shot differential ranking. Data on their zone entries and exits shows that they outplay their opponents in all three zones. The Rangers are also among the better puck possession teams, but the Kings have a clear advantage here.
With that being said, shot differential, while important, isn't everything.
The shots have to go in, after all.
Neither team posts an impressive shooting percentage. The Rangers' 7.9% shooting ranked 26th, and the Kings' 7.6% ranked 28th. Given how much random fluctuation there is in shooting percentage, we can't read too much into that small gap; the Rangers might have an edge here, but it's hard to be sure.
But there is a gap in how good they are at stopping the opponents' shots. Jonathan Quick is a good goaltender, but he isn't on Henrik Lundqvist's level. There's enough variability in save percentage that Quick could easily outperform Lundqvist over a short series, but after posting a higher save percentage than Quick in each of the last six seasons, Lundqvist is clearly the better bet.
The Rangers also have more of an edge on special teams than they're generally getting credit for. The Kings' power play has been red hot in the playoffs, but do you expect their 18.9% shooting to last? You shouldn't.
Looking at the longer haul, the Rangers have gotten more shots on their power plays than the Kings have and shot for a higher percentage. They've allowed slightly fewer shots on the penalty kill, and stopped more of the shots. And they've drawn more penalties than their opponents, whereas the Kings have done the reverse. The stats can't tell you what will happen over a small sample -- nothing can! -- but the best bet has to be that the Rangers have a significant edge here too.
Overall, the Kings are a dominant team at 5-on-5 possession, but the Rangers have a dominant goalie and have small edges in many other areas.