I format the drive depending on which platform (Mac/PC) is going to do the maximum read and write with data on the drive.
So, for example if I'm going to do a lot of work on a Mac, I format the drive on a Mac (as HFS+ with GUID Partition Table), and then on Windows use HFS Explorer or MacDrive to do the occasional read/write on a PC.
Conversely, if I'm going to do a lot of work on a PC, I format the drive on a PC (as NTFS), and then on Mac use Paragon NTFS to do the occasional read/write on a Mac.
This applies to editing with FCP7/X or Premiere Pro on Mac, or even working with Photoshop or Excel/Numbers.
If at all I run into a problem with files on a drive, I usually repair it on the native platform. Meaning, if an NTFS drive has problems, I repair it on a PC. Or, if a HFS+ drive has problems I repair it on a Mac. Never vice versa. To repair a drive on a Mac I use Disk Utility, or if that fails, then I use Disk Utility.
And, all my data is usually backed up in two places. I use Carbon Copy Cloner or ChronoSync to keep two drives or even folders on drives synchronised with the same data. For smaller files (like FCP/Prem projects or spreadsheets, documents, or even pictures) I use DropBox, Google Drive, or iCloud to keep a copy safe.
I completely avoid MS-DOS or ExFAT for shared drives, as they are problematic over a long period.