That second shot is less easy, if there's nothing in the foreground. Dunno really, could actually be a weird background, or something about the lens, or a bit of both.
You could maybe identify it as a lens characteristic by comparing directly against another lens. Assuming you don't have another 600mm, just use your longest other and enlarge to match - should be good enough to see if they're significantly difference.
You don't have a filter on the Tamron do you? That's a common cause of funny backgrounds with long lenses.