Which device size(s) do you use?
EPCS1-64 supports a 'Read Silicone ID' operation - EPCQ doesn't, nor does EPCS128.
Beyond that there is only the 'Read Device ID' command. However, both EPCS128 & EPCQ128 will return the same value. All other devices should be uniquely identifiable.
If in doubt reprogram with and image intended for an EPCS (x1). This will compromise boot time - a little - but nothing else. The configuration image is identical. The only difference will be the config flags early in the boot sequence telling the FPGA how to control the config device. However, if the FPGA controls an EPCQ as if it's an EPCS then all will be well.
Cheers,
Alex