Diablo 3's challenge level varies based on the difficulty you’re playing on. The game itself offers good reason to play on one difficulty or the other depending on the capabilities of your player character, your gear, and your personal preference of ease-of-play over challenge.
Reddit user d3agl3uk has drawn together a dificulty chart to help you identify the benefits of running the game at higher or lower difficulty levels.
In addition to monster health, monster damage and experience points, the chance for legendary drops increase exponentially at higher difficulties.
It should be noted that the percentages for Legendary crafting material drops is set to be changed, and will be in alignment with the droprate percentages of Death’s Breath in an upcoming patch for the game.
Information about legendary drop chance in T1 and T2 comes from a Blizzard post, which reads as follows:
So, the 25% bonus to Legendary drops in Nephalem Rifts is multiplicative and will actually stack with the scaling Legendary drop rate bonus in Torment 1-6.
This means if you're playing through a Rift in Normal-Master, you'll have a 25% bonus to Legendary drops. If you're playing through a Rift in Torment 1, you'll have a 43% bonus to Legendary drops (1.15 * 1.25 = 1.43). If you're playing through a Rift in Torment 2, you'll have a 65% bonus to Legendary drops (1.32* 1.25 = 1.65). And so on.
Hope that helps clear some things up a bit. (Also, I really hope my math checks out. >.>)
Note that we're going to continue to keep an eye on Rifts and how rewarding they are (or, more importantly, how rewarding they feel). We've already seen some great feedback from players on that topic that we're taking a look at now. This buff is just a small change we could make quickly, and we're definitely looking forward to your feedback over the next few days.
The chart is accurate, as of April 4, 2014.