I'm gonna go with not so much.
I was a fan of QR back in the Mindcrime and Empire era, but everything they've put out since has kinda been meh... Geoff Tate kinda lost his appeal for me after Empire. And while I think the new release with La Torre is a vast improvement, it's still not up to the quality of MK or Empire... so...
As for the DT side of things, I honestly don't think they would work well together as opener/main act. Both bands are too big commercially to fit as the opener, and if they co-headlined, DT would have to cut out some of their longest, most popular songs. Plus, I imagine they're touring with the orchestra, and that would be logistically very difficult to set up after tearing down QR's stage. The wait between sets would be far too long. (like waiting for the new album)
And yes, I'd put QR in the opener's slot, because without Geoff Tate, they have lost a lot of ground. While DT has continued to grow and improve over the years.