Q: Do FGPMMOUDG and FGPMMOPA6E/FGPMMOPA6E have the same patch antenna?
No, they do not.
The module FGPMMOUDG has a patch antenna coded GTPA008 whereas the modules PA6x have patch antennas coded GTPA010.
UDG and PA6B/PA6E use antennas from different manufacturers that best suited them based on their design, hence the differences.
All of them though are based on the same MedaTek 3329 chip.