1994 and before, World Cup semifinals often took place on the same day, so one team had only a few hours more preparation time than the other. When semifinals did not take place on the same day, the team with the extra rest day most often lost. Here is a list with the team with 5 days between semifinal and final first, team with 4 days second:
1966: West Germany - England 2-4 aet
1990: Argentina - West Germany 0-1
1998: Brazil - France 0-3
2002: Germany - Brazil 0-2
*2006: Italy - France 1-1 aet (4-3)*
2010: Netherlands - Spain 0-1 aet
*2014: Germany - Argentina 1-0 aet*
Only twice did the team with more preparation time win, and this team did not win in regular time. The latter instance of the two also seems to be the only time when the later semifinal went into extra time while the earlier one did not.
The very first world cup final was four and three days, resp., after the semifinals, and also won by the team with fewer time to prepare.
1930: Argentina - Uruguay 2-4
Interesting side observation: The third place match was won by the team in the same semifinal as the eventual champion every time except 1990 (host Italy came third after being knocked out by eventual final loser Argentina) and 2014 (Netherlands, despite professing lack of motivation beforehand, beat Brazil, who had apparently not recovered from a severe semifinal loss against eventual champion Germany).
While these may not be enough observations to establish that less preparation time is actually useful, one can likely rule out a significant advantage. The results of the four most recent European Championships and Copa Américas is in fact even: 2 wins each for the team from the earlier semifinal, 2 for the one from the later one.