rename() function apparently doesn't move files larger than 4 GB, even though the filesystem supports, when the operating system is 32 bits.
Tested here with PHP 5.5.9 (x86), in Linux environment (Ubuntu 14.04.5 LTS i686), with source file (60 GB RAR file) in ext4 filesystem and destination is a external HD with NTFS filesystem. Only 4 GB was copied and RAR was corrupted: "Unexpected end of archive".
Not tested if rename() can move files larger than 4 GB in 64-bit environment.