It will not run with any other series because of the driver dlls.
ps2000.dll works with 2000 series
ps3000.dll works with 3000 series
ps4000.dll works with 4000 series
The APIs for the different series are similar but not identical.
All the functions have the series as a prefix.
ps2000_open_unit() in ps2000.dll
ps4000OpenUnit() in ps4000.dll
Another issue is the way the sampling rate is set up, it is set as a divider from the maximum sampling rate of the open device.
If the device has a different maximum sampling rate (2000 -> 200MS/s and 4000 -> 80MS/s) the same timebase divider will give you a different sampling rate.