Gretzky

First and foremost let's supposed both teams have similiar talent/experience and they are neck to neck in the competition, that's where we can talk about home field/court advantage.

For basketball, baseball and football (the American/Aussie style) home field advantage is not as prominent as in soccer and ice hockey.

Example: Basketball
1) There are just too many factors in a basketball game now. Besides, the pace of the game is so fast that 1 second on the shot clock can make a difference. Home crowd support and the court (remember the Old Chicago Stadium/Great Western Forum?) used to make a huge diff. in games but their influence diminish overtime. Think about how many times you've watched a game where a buzzer beater (i.e. Reggie Miller,MJ) silenced the crowd? The Celtics/Pacers series this year is a good witness to that.

Example: Football
2) Football, in the contrary, is a different game. The pitch is custom made and can have major effect on visiting teams (the infamous tall grass of the old Wimbley Staduim in London and Arsenal's pitch). It's an outdoor game for the most part and the 'enviromental factor' plays a major role in the performance. In that sense, home team definitely has advantage over it. Russian, German, Mexian, Chilian teams use that to their advantage in their league games (hot/cold, snow/sun, hard pitch/soggy pitch, etc.)

Most professional team now have psychologists on staff and the booing of the fans are no longer major factors of the game. Advantages are often given to whoever has the fastest adaptability in real time.

That's why I always like what they do with the superbowl/champion's league final where they have a neutral site for the final game.