Depending on how far you want to shoot them, the .25-06 is one of the more capable calibers out there. We've got a couple in the family and while we haven't tried the Barnes, we're perfectly happy with the 117 Sierra Gameking and the 117 Hornady SST. They work fine on our Louisiana whitetail deer.
It seems to me that the 80 grain Barnes would work just fine. Years ago, the 87 grain .250 Savage was touted as wondrous whitetail medicine.