I don't think this is a fair comparison, honestly.
Of course Eddie can play Jimmy's material because he grew up listening to Zeppelin records and trying to imitate his style before finding his own voice. Whereas Jimmy grew up listening to blues men and early rock and rollers. This is how musicians have developed since the beginning of recorded music. While I'm not gonna say one way or the other who is better, I think this point isn't a fair one to make because by the time Van Halen became popular, Page was already accomplished and more interested in developing his own craft than imitating the style of others.
Eddie is much more technical.
Comparing Jimmy Page to Eddie Van Halen is like comparing Fred Astaire's dancing to the style of a Breakdancer. EVH completely redefined what an electric guitar could do. I prefer the style and grace of Fred Astaire, but I never saw him headspin or windmill, know what I mean?
It would be a more fair debate if Van Halen hadnt been held back by the artistic and technical limitations of his band. I mean the closest (and first to my mind) apples-to-apples comparison is "Heartbreaker" to "Eruption." One is a clear creative win while the other is pure technical win.
Jimmy has so much prowess and is able to convey so much through his playing, both musically and emotionally . When was the last time you heard EVH put a guitar in an open tuning and whip up something like The Rain Song or Black Mountainside/White Summer? Eddie was a teen when LZ1 came out. He saw them at the LA forum. EVH was raised in the 60's, he blossomed in the 70's. He was there as a listener to all the great 60's bands as it happened.
My conclusion is that EVH is one of the most technically gifted guitar players of all time, but Zep made better music in my opinion.