Obviously the fanbase issues are the same for most sports. Baseball adds two more factors: variable field dimensions and last licks.
Last licks are more of a psychological advantage, IMO. Both teams have an equal number of chances to score, but the home team gets a shot to catch up an win it at the very end.
Field dimensions affect both teams, but management can build a team to take advantage of their particular field's dimensions.
For instance, the Red Sox can load up on sluggers who hit the ball a mile high but not very far to left field. Those hits go over the Green Monster for home runs at Fenway, but are fly outs in most parks.
The Padres can hire strikeout / fly ball pitchers because their huge park allows the pitcher to give up a lot of fly balls without worrying about their being home runs. But when that team visits Citizen's Bank Park in Philadelphia, with short walls and the wind blowing out, what look like dinky pop flies in Petco become home runs.
Because the dimensions vary (including not just the outfield walls but foul territory), a fielder who plays frequently in a given stadium is more confident about how far he can go before bumping into the walls, and knows how the ball bounces off of odd-shaped corners (or the hill in Houston).
The ball may also bounce slightly differently on an infield, depending on how it's maintained, and it moves much more quickly on artificial turf, like some stadiums have. A team with a turf stadium may gain a home field advantage by sacrificing a little bit of offensive power to improve their infield defense, while their opponents who sign iron-gloved sluggers lunge helplessly after their seeing-eye grounders.
So yes, in short, home field advantage is probably a stronger factor in baseball than in football or basketball. But if you really want to quantify it, take 50 years worth of home/away win/loss data from each sport and see if the percentages are higher in one than the others.