As I mentioned, peak splitting due to detector overload is not always predictable. Also, USP-type methods are often very old, and were developed using equipment that have very poor performance by current standards.
As other have mentioned, the design of the injector, tubing length and diameter, and flow cell design can all contribute to band broadening. That is, they will cause the peak to be spread out over a larger volume. This will reduce the concentration, which means the peak height is smaller. If you compare an old Varian LC with a new Agilent LC, I would expect better peak shape (and taller peaks) from the Agilent system.
You should also check your detector settings for the Agilent. Specifically, verify that the PeakWidth (ResponseTime) setting matches the actual peak width in your chromatogram.
If you still have problems, write to us again. But first I would find a sample that causes splitting. Injected it four times to see if the splitting for the same sample changes for each injection. Then dilute the sample with an equal volume of solvent, and inject again to compare peak shape.