Maybe and maybe not. A good team could win the President's Cup merely by staying healthy and playing the other good teams during times when they were going through injuries, i.e., luck of schedule, but that does not make them the best of the good teams. Also, the best team on the last day of the season may be a team that made some great TDL trades, but their record earlier in the season wasn't so hot. There is also the factor that some teams can play games against random opponents and do very well, but they then have difficulty in a long series against a single opponent.
By contrast, the playoffs involve only the top teams all playing in a compressed time period, and there are long series between each of the teams such that the winner that moves on probably was the better team between the two.
The President's Cup is a nice honor to be sure, but IMHO it's just not even roughly comparable to the Cup in prestige. One comes with a huge parade thrown by the City, the other comes with 10%-off coupons at Olive Garden (mmm, warm breadsticks).
