Tempo is a way of maximizing possesions. When you go slow down you can will limit your opponents opportunity to score points. If you can keep the game close you have a better chance at an upset. When you play uptempo, it is generally because you think you have a major advantage in the game and you want to increase the number of possessions and scoring opportunities. Here's the catch, if you are a team that fouls a lot then playing uptempo may be trouble. Just like scoring opportunities, there are more opportunities for your team to foul, so if you have a short bench, this may not be a good option, ever.
As far as stamina is concerned, playing slowdown will maximize the number of minutes your starters can play. So when you have a decisive advantage in the game, but that advantage is with your starters, playing slowdown would keep them on the floor for more minutes.