I just couldn't leave well enough alone. First, comparing 1.3X Hawks to 2x Lomos is a waste of time; they're apples and oranges. You might as well compare 1.3X to Super Baltars for that matter, or Lomos to Zeiss Spherical Master Primes...
Here's what's going on with these lenses folks: the Lomos have an exggerated curved field of focus. ALL lenses have a curved field, but anamorphics have a very pronounced curve. ALL (front element) anamorphic lenses (Panavisions and Cookes too) have this curve (and front element anamorphics are the only ones that make any sense in the digital age). What happens is that as you open up the aperture you are decreasing depth of field; if you decrease DoF to the point that it does not cover the curved focus field, the lens goes really soft. It just so happens that the loss of focus begins in the corners and works inward as the DoF becomes smaller and smaller. This is why FAST anamorhic lenses are kindof a waste... unless you are clever with your framing.
You can see a great example of this effect of DoF/Curved FoF trading off in these tests. Again, it's really pointless to compare apples and oranges, but here it is anyhow. The next thing to consider is diffraction. You can't stop down anamorphics too far (not much past T11) otherwise you start to get diffraction past the edge of the iris blades. This occurs in EVERY lens, spherical or anamorphic; some have better performance than others. ND filters are a great way to overcome this problem.
If you want to shoot anamorphic by any lens manufacturer you should probably be looking at a T4/5.6 split on the aperture ring for your optimum performance. Light your set accordingly and you're cooking with gas. Open that puppy up like it was a spherical lens and you're going to see a loss in clarity; same if you're outdoors and shoot your sunny 16...