I've had Remington pumps in .243, 30/06 and 35 Whelen, plus shot a few in .270. All were shooters. The older 760s had different lay-out on the locking lugs, almost like an interupted thread. They may have been a little smoother in operation but the difference if any is small. The 7600 has 4 lugs. This appears to be the only difference.
I would put the accuracy level on par with out of the box bolt actions in similar price ranges. The way the pump is designed leaves the barrel free floating. You can play with your loads, but not the bedding. There isn't any. These rifles seem to stay sighted in forever, which is endearing.
My Whelen will stick 5 Hornady 250 gr Interlocks into thumb nail sized groups when I'm having a good day, groups over an inch are rare. The issued plastic buttplate was designed by Satan. Ouch! It didn't stay around long.
Extraction might get a little sticky on maximum loads since the action doesn't give any mechanical advantage. Cases should be full length resized for the same reason. If you are after a non-bolt gun the 7600 deserves a long look.
Dogleg