From a technical standpoint, Vai is among the greatest to ever walk the earth. The shit he does on a guitar and the fact that he does it so effortlessly will never cease to amaze me.
From a influential standpoint, Eddie ranks up there with the likes of some of the biggest names in rock guitar: Hendrix, Clapton, Page, Beck, Blackmore, etc. Not saying he invented anything (did any of them?), but his style shaped a new age of rock/hard rock in the late 70's and throughout the 80's.
---
That being said, Eddie is his own worst enemy. Being a dick to band members (other than his brother), being a dick to fans, being a drunken bum on stage (but lets face it, so was Hendrix and Page on a constant basis!) who was extremely sloppy at times (again, see Hendrix and Page for guys that perfected being imperfect on stage). But he has an arrogance about him that has turned people off over the years. He's hardly alone in the area. Superstars have been a pain in the ass for years, whether it be music or any other form of art, Hollywood, politics, etc. Eddie seems to play the same non-sensical solo that always leads into a sloppy-ish version of Eruption. You can watch videos from the 80's, 90's and 00's and see/hear the same thing. Sometimes it lasts 8 minutes, other times 10 minutes. I think people have definitely gotten bored with it, regardless of how iconic Eruption was in its day.
On to Vai, while the guy has a truckload of talent, he also is extremely weird and odd in his playing style. Not just once in a while, but quite a bit. I own nearly everything that he's put out and some of it I can't hardly listen to because he goes into this "space cadet mode" and seems to just make noise. Other times, he's just about the smoothest cat out there playing the stuff that he plays. I give Vai more credit in the solo department because he definitely does keep it fresh and doesn't just play the exact same solo for decades at a time.
Not sure how to vote here.
Vai wins on skills, it's not even close.
EVH wins on influence.
Going to abstain from voting for now.