Below you can see each team's Fenwick% on the season, since Feb 1 (~30 games), and since March 1 (~20 games), plus their 5-on-5 save percentage rank, 5-on-4 shots for/60 rank, and 4-on-5 shots against/60 rank. The shots for and against on special teams are pretty tightly clustered, except San Jose's power play, which is far and away the best.
This post from Objective NHL showing cumulative Corsi differential (score tied) is also worth a look.
I know which team I'm picking to win the West.
Canucks-Hawks will be a very close series, I think. Although the Canucks have been at the top of the standings for almost the entire season, while the Blackhawks needed Dallas to lose its final game to squeak into the playoffs, the Hawks haven't been able to win as many games as they should be able to, for whatever reasons. Nevertheless, I place much more faith in goal, shot, and Corsi differentials over records, and those all indicate Chicago is every bit Vancouver's equal at 5-on-5 (except in net). With some great percentages on special teams, Chicago will win this series. But otherwise, Vancouver should win. This is the worst 1st-round matchup Vancouver could have drawn, and unfortunately for them, it likely won't get any easier. Canucks in 7.
Sharks-Kings seems like it will be a pretty lopsided series. San Jose has been the best team in 2011 by miles, and with Anze Kopitar now out with an ankle injury, the only way San Jose loses is Quick-ly. I can't see that happening. San Jose is deeper than Los Angeles at every position (even in goal) and is better at nearly every position on the depth chart (1D seems to be LA's only advantage). I'll change it up here and go with Sharks in 4.
Red Wings-Coyotes too looks like it will be fairly lopsided. Phoenix's only advantage is in goal. Even with Henrik Zetterberg out, the Red Wings can possess the puck and shut down other top lines (thanks to having a back-up in Pavel Datsyuk). Strong special teams and good possession = win in spite of worse goaltending (which isn't a huge difference over 7 games). Red Wings in 5.
Ducks-Predators will be a series to keep an eye on. The Predators are much better than Anaheim, but the Ducks' "RPG" line (Bobby Ryan-Ryan Getzlaf-Corey Perry) is an absolute demon in possession, and Selanne and Koivu do a good job against toughs as well. Thing is, even Anaheim's top Corsi Rel players have negative Corsi Ons, meaning that Anaheim is being continuously outshot at 5on5. Trade deadline acquisition Jarkko Ruutu is the only Duck with a positive Corsi On (and that came before the trade). Between Shea Weber, Ryan Suter, and the Predators' wealth of good two-way forwards, plus Pekka Rinne, I think Trotz can mitigate the damage RPG does, and then jump on the rest of Anaheim's roster, which is pretty weak. If Hiller were playing, I might have been persuaded to pick Anaheim, but without him in the lineup I can't see any way Anaheim wins, barring superhuman performances from RPG and Selanne. I won't pick Nashville to seal the series on the road, so I'll go with Predators in 6.