You should ensure data integrity with checksums and/or hashes.

Yes. Ext4 is far better (including efficiency) than FAT. A very modern FS versus one of the oldest and terribly inefficient... Lol

FAT typically has large cluster sizes, especially on large volumes. Ext4 has relatively small clusters. A tremendous amount of small files could possibly explain it. Did you happen to enable any compression for the volume?

I would first check carefully that all the files were actually copied. Often the simplest explanation is the correct one, in this case that some files weren't copied for some reason.

That said, I have seen something similar once, and the reason was something called sparse files. We had some database backup files on a FAT32 partition (don't ask why), and we copied them to an ext4 partition. We noticed that the copied files occupied about 1/4 less space than they did on FAT32. Turned out that the backup files contained large amounts of "empty" space (zeros bacially) and because FAT file systems don't support sparse files, that empty space occupied physical disk space on FAT32. On ext4 however, those empty parts didn't consume any physical disk space and thus the total disk usage was way lower.

Does your data include disk images for example? If so, this could be the reason.

In general EXT4 is better than FAT in terms if its cluster slack (how much space is wasted by minimum cluster size) and it's also way better at handling problems related to power outages and interruptions than FAT filesystems are.

Its less about efficiency and just about compatibility at least in terms of fat and ext4. Ext4 is open and was designed for Linux, where fat was for windows and was closed off and hard for Linux to support

I'm not sure about the file size diffs, maybe different default compression levels or a incomplete copy?