How much higher is the legendary drop rate in the Torment difficulties?

From the diablo forums, the legendaries drop rate is not disclosed as of now.

Grimiku said: 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.

Legendary drop rate increases by 15% for every level of Torment (no change on Hard/Expert/Master) multiplicatively, and is further doubled while in Nephalem Rifts (source).

So the whole table looks like:

                                                              [   speculative   ]
           Norm Hard Expt Mstr  T1   T2   T3   T4   T5   T6    T7   T8   T9   TX
Overworld  100% 100% 100% 100% 115% 132% 152% 175% 201% 231%  266% 306% 352% 405% 
Rift       200% 200% 200% 200% 230% 265% 304% 350% 402% 463%  532% 612% 704% 809%

Baseline drop rate is not known, though.