Effects of copy (cp) vs cut (mv) on file systems

When you have to move a file to a different location in the same file system, you have two options: just cut-paste (or mv), or copy-paste (cp) and then delete the old copy. I'm wondering what are the effects on common Linux file systems (especially ext2/3/4) in terms of possible defragmentation and long-term file system health and efficiency. In other words, no matter which option is faster (of course mv is faster than cp), if you wanted to keep your file system as clean and efficient as possible over time, should you prefer mv or cp/rm when moving a file? Does it even matter in modern file systems?