Since the 2005-2006 NHL regular season, penalty shot opportunities consistently yielded a higher conversion percentage of goals made than power play opportunities.

*graph does not include data after the 2012-2013 NHL regular season
2015-2016 NHL regular season (82 game season):
Penalty Shots -- 16/58 = 27.6%
Power Plays -- 1429/7658 = 18.7%
2014-2015 NHL regular season (82 game season):
Penalty Shots -- 14/41 = 34.1%
Power Plays -- 1403/7520 = 18.6%
2013-2014 NHL regular season (82 game season):
Penalty Shots -- 21/69 = 30.4%
Power Plays -- 1441/8055 = 17.9%
2012-2013 NHL regular season (48 game lockout-shortened season):
Penalty Shots -- 8/34 = 23.5%
Power Plays -- 872/4785 = 18.2%
2011-2012 NHL regular season (82 game season):
Penalty Shots -- 27/69 = 39.1%
Power Plays -- 1408/8132 = 17.3%
2010-2011 NHL regular season (82 game season):
Penalty Shots -- 27/78 = 34.6%
Power Plays -- 1571/8179 = 18.0%
2009-2010 NHL regular season (82 game season):
Penalty Shots -- 16/55 = 29.1%
Power Plays -- 1664/9136 = 18.2%
2008-2009 NHL regular season (82 game season):
Penalty Shots -- 23/59 = 39.0%
Power Plays -- 1938/10227 = 18.9%
2007-2008 NHL regular season (82 game season):
Penalty Shots -- 19/64 = 29.7%
Power Plays -- 1871/10536 = 17.8%
2006-2007 NHL regular season (82 game season):
Penalty Shots -- 25/70 = 35.7%
Power Plays -- 2099/11935 = 17.6%
2005-2006 NHL regular season (82 game season):
Penalty Shots -- 35/103 = 33.4%
Power Plays -- 2545/14390 = 17.7%
(goals made/opportunities)
Notice the range for penalty shot conversion percentage during 82 game seasons is 11.5% (39.1 - 27.6) and the range for power play conversion percentage is 1.6% (18.9 - 17.3).