Some googling gives me these possibilities:

- Spotlight is trying to index the external drive as you're using it. They say go into the privacy settings under Spotlight in System Preferences and add the external drives to the list of ignored drives.

- It may indeed be the FAT32 file system on those external drives. The problem is that you're transferring from Mac to PC, and that's the expected format that you'd use for that job since it's writeable and readable on both Mac and PC. NTFS would be faster but that's not writeable from the Mac. This article suggests using ExFAT, but this other page suggests that you should only use it if your external drive is a flash drive, or else it will also be slow.