Personally I wouldn't suggest this. It has been my experience (and that of others online if you want to search around) that exFAT is only really reliable for things like thumb drives. I would never suggest using it on a 1 TB or larger drive. The format is still young and runs into a lot of permission / corruption issues when used to hold a large number of files.
Although it's not a free option like exFAT I would suggest getting effectively format codecs. Personally I prefer to format drives for mac and install
macdrive on my windows machines however if you want to keep the drive as NTFS there are mac options such as
Paragon NTFS and
Tuxera NTFS. Free mac options exist but haven't been stable since Lion so use at your own discretion.
Again, this is just from personal experience as well as what we use at my work (film post production). Sometimes exFAT works great but when it doesn't you can lose everything so, IMO, it's safer to format the drive for one system or the other and go with one of the above applications.
P.S regular FAT32 works on both systems as well but has many documented limitations such as slow speeds and a 4GB file size limit (drives can be up to 2TB mind you)