I think he is extremely over the top criminally overrated. I personally don't like what the White Stripes did, specially Jack White. I tried to think why he is usually regarded as the best new guitarist and one of the all time best and really, the only reason I can think about is that the White Stripes, and especially Jack, tried to go back to rock basics. They went all the way to the 50s and 60s and revisited the whole blues rock thing that died a very long time ago with Clapton and other artists.
Basically blues rock is lead by a great guitarist and the very reason of this genre is the improv it requires by its lead guitarist and the rest of the band. Since the "rest" of the band is a crappy drummer, then Jack is the lead band member. The only band I can think of that played a very fair amount of blues in the last 10 years was The White Stripes, and at the same time achieved critical commercial success with other kind of songs.
This means to the music listeners of "nowadays" that are only drooling for mainstream alt. rock hits, the blues of the White Stripes came as such an awe.
I think Jack can play guitar, but as to be elected the best guitarist since Jimmy Page is pure bulls*it and unfair.
If music listeners who are all over the commercial radio hits go back to the 60s and 70's and check out Ten Years After, Cream, Allman Brothers Band, Creedence Clearwater Revival and tons other and Led Zeppelin's "deep, underground and unknown" catalog, then they should know what a guitar player really is about.