The Browning P35 was always made by FN. Calling it a "Browning" was always something of a stretch, since John Browning died while developing the pistol. The original Browning design was rather unlike what we now know as a P35/Hi-Power.
The P35 was mainly designed by Dieudonne Saive, the FN engineer who also designed the FAL battle rifle. FN produced the gun, along with various licensed and unlicensed copies. The company called "Browning" is a subsidiary of FN.
The CZ75 has double-action capability the P35 lacks, but is not quite as slim and compact as the P35. The CZ75 is more reliable and less expensive. P35 magazines are less expensive and easier to find, and P35 holsters are more common.