This assumes you have listened to a decent amount of bootlegs or have concrete memories of the shows on the tours. The tours to choose from are 1974-77 Club Days, 1978 first world tour, 1979 World Vacation Tour, 1980 Invasion tour, 1981 WDFA tour, 1982-83 Hide Your Sheep tour, 1984 tour, 2007-08 tour and 2012 A Different Kind of Truth tour.
My rankings:
1) 1982-83 Hide Your Sheep tour--awesome setlist, the SGMAD jam, those great South American shows where they really opened up the playbook with the covers and everything. I just love that tour.
2) 1978 first world tour. Incredible sound that they'll never match again, plus they were so hungry. Despite the mostly short shows as an opening act the performances were unmatched in their history. Plus they did have some longer shows like in Japan where they did songs that would appear on VH II.
3) 1979 Invasion tour. More of the same from 1978; guitar sound not quite but almost as good as 1978. I'm splitting hairs really.
4) 1981 Fair Warning tour. Love all the FW songs as well as the performances of Romeo Delight. EWS and ICM chewed up too much of the concert though.
5) 1974-77 Club Days shows. They hadn't arrived yet and were doing loads of covers, but there was a lot to like such as songs like "Bullethead," "Let's Get Rockin'," "Show No Mercy" and those really early versions of "Runnin' with the Devil" and "In a Simple Rhyme."
6) 1980 Invasion tour. Very good tour though the tuning makes it more difficult for me to listen to these shows than the other tours. If not for that it probably would be higher. Interesting setlists too with "Women in Love..." and "Bright Lights Big City," not to mention "Light Up The Sky" for the first half of the tour. This was also the first tour in my opinion where Roth became Roth and settled into being the raunchy guy he gained a reputation for.
7) 2012 A Different Kind of Truth tour. I can't put this above any tour except 1984 just because of age but Eddie is absolutely shredding and playing as well as he ever has. They feel like a true band again and the deep cuts are back!
8) 2007-08 Reunion tour. While the static setlist got a bit tiresome, and Eddie had issues, it was still one of the best comebacks in rock and roll history. While they didn't play many true deep cuts, it was still a very good setlist that hit Van Halen I very hard, and there's nothing wrong with that.
9) 1984 tour. The only tour where the hype and party atmosphere was better than the show itself. It's still classic VH but in my opinion it's clearly the weakest of the tours. They weren't a band at this point. I didn't like the guitar tone at all, o course the keyboards were a negative, Roth's ego was sky high and he thought he was a full-fledged comedian by this point the setlists mainly focused on VH I and 1984 with little in between.