Flash Drives back and forth PC to Macs Question

I notice that some of my flash drives are FAT16 and some are FAT32.
Their general use is on the IMac, but every now and then I need to carry
a file on over to the PC. I'm not having trouble doing this. My question
concerns whether or not there is any advantage in using FAT16 over 32
or visa versa?
Also, I'm getting a lot of feedback from various sources that are
telling me not to use the formatting utility on the Mac but rather to
reformat the flash drives on the PC for a "better" format if needed.
Any validity to this at all? I think I noticed that the Mac disk utility
for the MS DOS format is a FAT16 and the PC choice is FAT32 for the
Flash drive format. Did I remember this right and is this perhaps the
reason for the confusion??
Many thanks

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Dudley Henriques