If I have LabView FPGA code made on NI cRIO-9082, but I want to run it on NI cRIO-9064, would this create any issue? They appear to have different Xilinx FPGA chips. If I install the same LabView and FPGA driver versions, would the FPGA hardware still be incompatible?
You need to replace the cRIO target in your project by the new type, then you need to recompile the FPGA code.
Given the very old 9082 hardware you also need to recompile the RT software as the new one uses a different OS...
The FPGA bitfile needs to be compiled for the hardware in question. So you have to recompile it in a LabVIEW project inside a target for your new hardware.
If your VI will recompile without issues will also depend what specific features you reference in it. Not every cRIO hardware provides exactly the same standard IO signals.
Also the RT executable will of course have to be recompiled too. Your cRIO-9082 runs Phar Lap ETS on an x86 CPU while your cRIO-9064 runs NI Linux on an ARM CPU. The resulting rtexe program from one platform is nothing more than a bunch of meaningless bytes for the other.