But, files can change size moving from one file system to another. It won't be anything radical but it will happen.
Then it isn't a copy. Copying or moving files should change nothing.
It is possible for total file size to change slightly when copying files from one system to another. It will normally happen when there is a major change in disk capacity and/or filesystem type. It can also depend on how the file's size is reported. Different file systems, such as FAT, FAT32, NTFS, or EXT3 for example, use different block sizes, the block size is also dependent on the partion size. The block size is the smallest sized block of data that can be written to disk. A file that contains 1 byte of data, and one that is at block size, will occupy the same ammount of disk space. Very often the file size is reported as the actual number of Bytes of used data, but sometimes it will be reported as the size on disk. If you change system so that you now have a significantly different block size, you can quite easily change the actual size on the disk. The data stored will be the same in each case.
This was much more significant when the file system was based on 8 or 16 bit data structures. Now we are using 32 or 64 bit data structures for the filesystem that is less of a problem. For example a 16 bit file system can only hold 65536 address locations, which is also the maximum number of files possible. In this case a 256MB drive would have a block size of 4096 bytes (4KB). So the smallest file you could have is 4KB. With a 32 bit file system you get 4,294,967,296 addresses and a 4KB block size would give you a 16 TB drive. Under a 16 bit file system you would need to use a 16 KB block size to have a 1 GB drive, while a 32 bit system could comfortably address that to the byte. Actually a 32 bit system can address a 4 GB drive to the byte. Oh and a 64 bit system has 1.84467441×10^19 addresses avilable (add 11 more zeros to the end, and move the decimal point all the way over to visualise how big that is). I think we will be OK with 64 bit systems for a while, but I as I remember thinking 16 bit systems seeming to be huge, maybe I shouldn't bank on them lasting too long.