I have a Mac laptop and a Windows desktop and edit my photos on both. I use a WD USB drive to store my photo files and LR5 catalog on.
I tried this using exFAT but found that it corrupted fairly often. exFAT is meant to be used with flash drives. I was always able to recover using disk utilities but it got tiresome and sometimes worrisome as the recovery took multiple tries. I always had backups but would rather not go through the hassle of using them. According to Wikipedia, "The standard exFAT implementation is not journaled and only uses a single file allocation table and free space map. FAT file systems instead used alternating tables, as this allowed recovery of the file system if the media was ejected during a write (which occurs frequently in practice with removable media)."
My experience was that this happened fairly often even though I was very careful about ejecting the disk and cautious about moving cables while using the disk.
I switched to FAT (I know that's not what you want because of smaller maximum file size) and now have no problems.
If you decide to go exFAT be sure you have a good and often used backup procedure. YMMV.