It depends on the workload. Copy-up is more expensive than snapshots. If it's ext4+overlayfs, then copy-up is really expensive (full file copy), whereas if it's btrfs or XFS then it's reflink copies. Much more efficient. But btrfs snapshots in effect are instant reflink copies. But then overlayfs has the benefit of shared pages.
Also, at least Btrfs snapshots are more logical, like files; than physical, like blocks. Whereas LVM snapshots are separate (logical) block devices, Btrfs snapshots are file b-trees on the same file system.
Maybe the overlay2 graph driver (the driver used in Docker or Podman to interface with the kernel) is getting more usage and thus maturing more quickly, compared to the btrfs graph driver? I think upstream Docker/Moby are defaulting to the btrfs graph driver if /var/lib/docker is on Btrfs. Meanwhile on Fedora where Btrfs is the default for desktops, and Cloud edition, Podman defaults to overlay2 graph driver no matter the underlying file system.