I understand where you're coming from, but no offence... Evile aren't the next big thing. They will never be the next big thing, because unlike the days you're talking about proper metal isn't as popular as it once was.
I know this doesn't accurately reflect ticket sales but lets compare the two band's last.fms
Evile: 33,841 listeners, 504,889 plays
Trivium: 458,922 listeners, 17,726,952 plays
It's pretty clear who has the bigger fan base... that's why I think Evile would be the band befitting most from the tour (by gaining new fans). Though admittedly it would be good for Trivium to tour with a band like Evile because it would give them a kick up the arse. In my opinion mainstream metal at the moment is ruled by two bands. Trivium, and Mastodon, nobody else comes close.