I can say for sure 1920x1080 shouldnt be a problem.
My game is using that resolution,
with a background picture size of 7000x1080,
another picture with 9200x1080
and then ca. 2000 objects.
Everything with 60fps.
So, looking at your pc specs, i would say, that the factor,
probably is your older pc.
But i could be wrong, you should wait for more people,
that may have an answer ;)
//Edit: Try what Sqiddster said, best way to test :)