If the axis limits problems include A4, there is a good chance that singularities are involved For singularities a slightly different robot model, tool/base values etc. can cause a significant deviation between physical and simulated robot.
As the first step I'd suggest a quick plausibility check: Choose a (= one) position somehow representative of the area that is causing errors.
In the advance settings, tick the box "Skip End position" / "Halt at end position" (depending on KUKA|prc version) and run the program. The robot will stop at exactly that position.
Then compare the axis values shown in the simulation with those on the physical robot. If they are not very close, double-check tool and base values and the robot type.