The 10% 3 times is arguably better than 3 turns and then 30% and arguably worse, assuming you can use extra turns after a success to do other things. Although there are values for which this changes, especially depending on how risk averse you are.
Take your d6 example
There's obviously a 50% chance for the second option on the effective "roll 3"
For the other option, the combinatorics gets a bit more complicated.
First roll, 6 options. 1/6, 17% chance
Second roll, 6 options (36 combinations of which 6 are already successful from turn 1, and of which 5 more are now ALSO successfull) 11/36, 30% chance by round 2
Third roll, 6 options (216 combinations, of which 66 are already successful, and of which 25 more will be successful) 102/216, 42% chance by round 3
So you've got a slightly reduced chance of overall success, but a greatly increased chance of getting success on an earlier roll.
For the original example...
Lets say it's 3/10 and 1/10 to make it a bit easier.
Option a:
Round 1: 0%
Round 2: 0%
Round 3: 30%
Option b:
Round 1: 10% (10 combinations, 1 success)
Round 2: 19% (100 combinations, 10 success from round 1, 9 more from Round 2)
Round 3: 27% (1000 combinations, 190 from round 1 and 2, 81 from round 3)
This is, of course, ignoring any potential benefits from inflicting the effect multiple times, in which case multiple attacks is hands down the winner.
And assuming I remember my combinatorics correctlys.