Had both an xtrIII 3.3-18 and the vortex Razor LHT 4.5-22 on my wife's 7 max hunting rifle. For the price of the burris now, they are a great deal. The vortex is more money, but still worth it imo. They both have a similar feature set.
Being ffp and not illuminated was not the best combo when timber hunting elk on low magnification, the vortex is better in that arena, being illuminated. The vortex also had slightly better glass in both of our opinions, however both were plenty for long range use. I used my wife's rifle with the Burris on it to take a cow elk at 1032 shortly after first light, and was not hindered by it, though I do like the extra magnification of the vortex.
The Burris had a more tactical feel, the vortex more hunting. Turrets on both are fine, the vortex having a little less feel, but I don't care if a turret is a little mushy, I don't dial my scope by brail, I look at it. Your needs may be different for something like PRS. The lines match up well on both and both were repeatable. I like the turret design of the vortex better for hunting, lifting, turning and locking wherever. We zero our rifles at 100, but while out hunting, dial them to MPBR (up about 2-2.5 MOA), so if we come up on a elk at 250, we don't have to mess with zero, just shoot. For this, the vortex is a better design.
Obviously the vortex is lighter. It also has the more common 30mm tube, vs 34, which slightly limits some mounts. Not a big deal, but something to be aware of.
The one part that I really liked about the xtriii, is it was built in USA.
Overall, her rifle now wears the Vortex. The extra weight of the burris and it's mount made it a good bit heavier for my wife, the feature set between the two is similar enough, and for hunting use, the vortex is a little better in these aspects - better glass, illuminated, better turret design.