I think it depends on the team and the market. If we stick to the Patriots/Lions comparison, the Patriots should obviously be trying to put a competitive product on the field at all times. Since the team recently won a few championships, the expectation is that they continue to compete at the highest levels. For the Lions, they should really be making moves just to get to the show once and then build from there. In addition to spending money, teams need to compete to lure free agents. The same goes for basketball, where one player can make all the difference (see also James, Lebron).
Although this point really doesn't hold for baseball or hockey. Those two sports seem to be places you can develop long-term with homegrown, cheap talent and be competitive at the highest levels.