There are two HD 6570s; one is relatively ordinary, and the other is comparatively weak for gaming. One has GDDR3 VRAM, the other has the up to date GDDR5 VRAM. Both the HD 5750 and the HD 5770 have GDDR5.
The HD 5750 is the slower of the two HD 5700s, and it is approximately 2 - 1/2 times as powerful as the weaker of the HD 6570s is.
http://www.gpureview.com/show_cards.php?card1=655&card2=616
The HD 5770 is still a relatively high performance video card, unlike the pair of HD 6570s.
It is above twice as powerful as the better of the two HD 6570s, the one closest to being a real gaming card:
http://www.gpureview.com/show_cards.php?card1=653&card2=615
Given the proven ineptitude of the Bethesda people, they also probably thought that the six generation number was meaningful, when it actually is not, and their automatic settings are probably wrong in each case.
Be that as it may, uninstalling the current graphics driver is likely to way to clear it up.