In my experience Storm Combo has had a lot of trouble beating Mentor decks ... but I suspect there's a few ways to build Storm and a few ways to build Mentor, and they probably line up in different ways.
I'm still new to Storm, Jesse Martin if he's made the jump to the new site would be the best reference I could think of to talk about this MU, but Ive been playing Mentor for a while myself and have some thoughts.
Mentor is a deck that does a fair amount of dicking around, just cantripping and running through their deck. When the mentor actually hits the board, it can get ugly quick, but even a turn one mentor off of lotus followed by some cantrips might not be enough against storm. If storm can get their Therapies and Duress off to pick apart the permission, then it doesn't really matter how many monks are on the board.
I look at it this way, as the Storm player: 4 Misstep, 4 Force, 1-2 Flusterstorm. Whether mentor is your wincon, or oath of druids, or Delver or whatever, that's what I have to punch through in order to resolve my spells against pretty much any blue deck. In game 1, unless I am worried about getting lightning bolted or something, blue is blue, the counter package is what matters, and the rest is largely irrelevant.
It gets more interesting post board, because white gives access to some strong hate cards like Stony Silence, Aegis of the Gods and Rest in Peace. Traditionally, Hurkyls was the SB card that got loaded up on for Shops, but with the restriction of Lodestone and the further rise of Mentor and their non-artifact SB hate, maybe chain becomes more of a priority.
Part of the reason I like Storm against Mentor is because storm doesn't care about the Mentor or the Monks. Oath can run into trouble because the mentor and his flunkies can punch through Griselbrand and the 7 life you gained when he blocked, your Mentor and Monks outclass every threat in a delver list, but Storm just doesn't care so much.