*math hat on*
As with a lot of probability problems, it really depends on exactly what question you're asking, and what the assumptions are. If we assume that you're, are planning to use the power if you miss, and want to maximize, before you roll the die, the odds of eventually hitting, here's what I found: (New to this forum and don't know the table formatting, sorry)
The difference is never major, but the elf has a slight edge if you need a 15 or less to hit, which you should in non-ridiculous cases. For instance, if you need an 11 to hit, the human hits 70% of the time by rolling a 7 or higher on his one roll, and the elf has two 50/50 shots, and thus a 75% chance of making both. The elf never gets more than 5% ahead, though.
Human actually does better if you need a 6 to hit (He needs anything but a 1, and the elf only has a 93.75% chance), but if you go lower, the human's odds can't go above 95% because you always miss on a 1, while the elf's chances keep climbing.
(If you look at percentage of misses or percentage of rolls where the power will make a difference, you get different numbers. And since you have some ability with Human Versatility to not use it if you suspect/know you won't succeed, that's a slight advantage to the human.)