From the diablo forums, the legendaries drop rate is not disclosed as of now.
Increasing the difficulty will increase the amount of damage that monsters do, give them extra health, and reward you with more gold and experience. Torment difficulties I - VI, however, also give you an better chance to find a Legendary item, and that chance scales up with difficulty. Here's the breakdown for most of the difficulty changes that's in our game guide. Remember, monsters scale with your character, so you'll normally be fighting monsters your level, or the party leader's level in a multiplayer game.
Normal: +0% Health, +0% Damage, +0% Gold Find, +0% Experience
Hard: +200% Health, +130% Damage, +75% Gold Find, +75% Experience
Expert: +320% Health, +189% Damage, +100% Gold Find, +100% Experience
Master: +512% Health, +273% Damage, +200% Gold Find, +200% Experience
Torment I: +819% Health, +396% Damage, +300% Gold Find, +300% Experience
Torment II: +1311% Health, +575% Damage, +400% Gold Find, +400% Experience
Torment III: +2097% Health, +833% Damage, +550% Gold Find, +550% Experience
Torment IV: +3355% Health, +1208% Damage, +800% Gold Find, +800% Experience
Torment V: +5369% Health, +1752% Damage, +1150% Gold Find, +1150% Experience
Torment VI: +8590% Health, +2540% Damage, +1600% Gold Find, +1600% Experience
Reading the whole thread of the forums, the difference of drop rate seems low enough to not warrant that a fast run would get you less legendaries than a slower at a higher difficulties. If you make a run at Normal a lot faster than at Torment 1, stay at normal. You might wanna try Master or Expert since the differences shouldn't be drastic if you can run T1.
If it only takes you 10-15 more mins at T1, go with T1. Only with tries out will you know which setting will net you more legendaries. For my part, I'll be lowering to T1 since T2 is a tad too slow for my taste even if I got 4 legendaries in about 4-5hrs of play.