Best external hard drive format for use with mac and windows?

This is more of an apple operating system combined with windows operating system question, but being that my OS will upgrade an fluctuate there is not option to choose in the operating system section.

Anyways to the question(s)

This whole prbolem came about when my computer started having issues, I want to back it up and whether I can continue to use my laptop or not I will still be owning an apple in the future. I went to buy a hard for back up and got told that it is not as easy as one would think to transfer files from mac OS to windows OS and vice versa. I have a mac, my boyfriend has a windows computer; we share files. Mostly I just copy his files, but once in a while I give him files too. I have read up and talked to people and only found one solution so far to format the external drive to fat 32 or exfat. I think only mac has the exfat option, but works well between both OSs, correct me if I am wrong.

What is the difference between fat 32 and exfat?

A user posted some good info about formatting. More specifically .Drives, partitions, formatting w/Mac's + PC's
https://discussions.apple.com/docs/DOC-3044

If I do not want to use fat32 or exfat is there a format type that works great for mac saving that I can still at least save files to that were originally on a windows computer? Such as I copy his files from his external drive to my computer and then save them to my external drive.

Is there a better format for file sharing between mac and windows that does not set a 4GB limit?

And a silly question, Can you dual format a hard drive?

Note: This format is for an external hard drive.