For a server, I would recommend ZFS without hesitation. Data integrity is
at the heart of ZFS which makes it a very good choice for backup storage.
It provides many features that ease the storage management. Quota,
compression, configurable record size, configurable sync writes, raidz,
snapshots, etc.
For an external storage, like a USB drive, I would probably pick BTRFS for
interchangeability reason. ZFS might still be used for an external drive,
but required the installation of ZFS on Linux to be working which is not
installed by default. While BTRFS is shipped as part of Linux Kernel. So in
case of emergency, you might plug the disk in almost any Linux computer and
get access to your files. BTRFS provide checksum and copy on write feature
that you want to ensure data integrity. But I would not recommend BTRFS for
any RAID setup. RAID5/6 is known to be buggy for a couple of years. I would
not trust my data on a BTRFS RAID. But for a single drive it's a very good
alternative to ext4