Not all fluorochromes have the same performance, so you will not
detect the same antigen with the same antibody coupled to
different fluorochromes.
Here is an example found in a supplier's catalog:
Therefore you should choose your fluorochrome carefully. The
lowest represented antigens should be revealed with antibodies
coupled to fluorochromes that have the best yield, keeping in mind
that some instruments cannot measure certain fluorochromes.
Remember that the yield decreases in this order for these
fluorochromes:
APC > PE > PE-Cy5 > PerCP-Cy5.5 >> FITC >>
PerCP
To help you to choose, here are several links :
A free open-source site with spectra of a multitude of
fluorochromes and in particular fluorescent proteins : https://www.fpbase.org/spectra/