Hey,
Borderlands 2 is one of the few games I've had weird issues with and for me that tied in with the FPS and VSYNC settings.
*If I recall correctly, even though I have a 60Hz monitor, setting to a 60FPS CAP caused weird stutter. I think I'm at "UNCAPPED" with VSYNC ON. That does cap it for me at 60FPS so I'm not sure why the difference but there is a HUGE difference for me with lots of stutter.
Other options:
a) Drop the quality settings to lowest for now (should be way above 60FPS), mess withe CAP (UNCAPPED again I think is best) and VSYNC until you're sure that's smooth.
then
b) Use RADEONPRO and try using Dynamic VSync (same as NVidia's Adaptive VSync I believe). That should make enable VSYNC ON provided you can output the target refresh or higher (i.e. 60FPS) but if you drop below then VSYNC is automatically off (screen tearing but no mini-stutter caused by synch mismatch).
*for b) if you get screen tearing too often then you're dropping below 60FPS (confirm with FRAPS). If that's annoying you, adjust a few quality settings to keep the frame rate higher.
I can't speak for RadeonPro, but if it's the same as my NVidia solution then forcing any VSYNC solution like "Dynamic VSync" overwrites any game choice for VSYNC (but not sure about the "cap" value as I rarely see that). In fact, it seems pretty stupid to give me options like 120FPS I can't even support so probably some coding issue there... hence possibly why "UNCAP" seems to work if I remember correctly. Again, experiment.
OTHER:
1600x900 may, I say again, MAY be a better resolution for you. The total experience is a combination of settings so it's up to you to decide what's optimal. Going above 1600x900 is often mostly reflected by the HUD and onscreen text more than anything else. So that gets a bit blurrier but you gain performance either for the frame rate or to increase quality elsewhere.