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Why is it harder?:
1) Chances
There are 16 teams in playoff contention, only other sport that can claim the same would be the NBA. The NFL only has 12 teams entering the post season, four of which get first-round byes.
But in the NHL, just because you finish first or second doesn't mean you get to skip the first round.
The MLB only has eight teams in playoff contention, therefore at the end of the season each of those eight teams has a 12.5% chance at winning the series. On the other hand, NHL teams entering the first round only have a 6.25% chance.
2) Duration
The winner of the Stanley Cup has to play a minimum of 16 playoff games, and may have to play up 28 total before deemed a champion. Once again the only other league that can claim the same is the NBA. However the NBA just recently, in the past few years, changed their first round format from five games to seven.
The two teams participating in the Superbowl will have played at the most four total playoff games at the conclusion of the championship. A large amount only play in three games in route to a championship.
MLB only has three playoff rounds, consisting of an opening round five game series and two seven game series'. The most one baseball team would have to play is 19 games, just three more than the Stanley Cup Champion's minimum amount of games.
3) Money
All though both the NBA and the NFL have salary cap's that regulate team spending just like the NHL has, the NHL has the lowest cap of all three leagues. Teams are only allowed to spend 50.3 million dollars when piecing together their rosters. The NBA's salary cap is over eight million more, and the NFL's cap is a ridiculous 116 million dollars.
In both the MLB and the NBA, teams in the larger market's draw in more crowds, therefore make more money, and attract more of the league's marquee players. Just take a look at some of the most recent champions of these two leagues.
Recent winners in the MLB include: The New York Yankees, Los Angeles Angels, Chicago White Sox, Boston Red Sox, St. Louis Cardinals, and the Philadelphia Phillies.
Other than the Rays, who were a surprise playoff team this past season, typically the larger market teams make the playoffs more often then not.
Recent winners in the NBA: Boston Celtics, San Antonio Spurs, Detroit Pistons, Los Angeles Lakers.
The bigger cities have fared better than teams like the former Seattle Super Sonics turned Oklahoma City Thunder, or the Minnesota Timberwolves, the Milwaukee Bucks, or Memphis Grizzlies.
However most recent Stanley Cup winners include: The Tampa Bay lightning, Anaheim Ducks and the Carolina Hurricanes. These are team's that play in a region that doesn't garner a very large hockey following.
But we have also see recent winners such as the Detroit Red Wings, and the New Jersey Devils who traditionally have had a healthy following of hard-core hockey fans.
The point being, that unlike other sports, you cannot buy a championship.
4) Injuries
The NHL is the only major professional sport that allows fighting. The players who participate in such actions may not disclose any injuries, but the wear and tear on an NHL player's body in 82+ games is more than that of a player in any other sport.
There is similar physical contact in the NFL, but the MLB and NBA don't even come close to the type of physicality endured as a player in the NHL.
All sports have endure major injuries to big-time players but the NHL clearly deals with more minor, nagging injuries than any other sport.
5) It's a TEAM game:
Lebron James single handily got the Cavaliers to the NBA finals. Sydney Crosby wouldn't have gotten to the finals if he didn't have all-star quality teammates in Evgeni Malkin, Marian Hossa, Ryan Whitney and Sergei Gonchar.
The Celtics won the 2007 NBA title with the "big-three." You will never see a Stanley-cup champion boasting that they have a "big-three," it doesn't happen. Three players will not win a team the Stanley Cup.
In the End:
The team that wins the Stanley Cup will have won their league title despite only having a 7% chance at winning the tournament, will have played more play-off games then required by most other sports, have endured more physical pain than any other sport, for a longer period of time, and will have done so using less money than any other professional sport.
Call my final analysis on a run-on if you like, but hey that's how the Stanley Cup is won, it runs on and on and on.
. There's probably only two interesting series (Celtics/Hawks, Clippers/Grizzlies). The rest really aren't worth watching. 
