I dunno really, Mikasa is barely in Index and rarely does anything even when she is.
The major difference between the two is scale. Index has a grand scale, involving epic take over/destroy the world plots and wide ranging ancient conspiracies on both sides of the Magic/Science divide. Railgun is more down to Earth, involving plots largely incited by small groups of people entirely on the Science side, in between a lot of slice of life stuff. Accelerator is looking to be a sort of mix of the two.
It will honestly just come down to preferences. I like epic plots myself but find Touma really dull and uninteresting while I love Mikasa, so I prefer Railgun. I'd suggest seeing the first seasons of both and seeing which, or both, or neither, you want to continue with. (Don't start a Certain Scientific Accelerator until you've done the Sisters arc in at least one of the other two shows first though)