Windows 7 - Can any Sync Program exactly make the same of A to B

I am using SyncToy.

I am choosing Syncronize, it is not renaming the files, it is usually creating new ones.
Same with Echo. And when it is creating new ones, it doesn't delete the old files, so I am having unnecessary duplicates.

For example;
I am moving files from A:\F1 to A:\F1\F2

The program creates B:\F1\F2 and creating new ones there, but it is not deleting the files from B:\F1. (It should be renaming instead of creating new, and even if it creates new ones, it should be deleting them from B:\F1 because those files do not exist in A:\F1 anymore.)

I am looking for a program that will rename the files as

Source file: B:\F1\File1
Destination: B:\F1\F2\File1.

Does anyone have any suggestions?

I am open to shareware programs as long as they work. I tried few of them before, they worked so slow or using so much performance - even though I have C2D 2.53 and 6 GB RAM-. I also have Toshiba's, Seagate's and WD's Backup Programs. I never used them, but if anyone has used and got good results, I will give them a try.

I am really tired of creating hundreds of GBs of data.
Copying a 2 TB Disk to another is taking more than a day with USB 2.0.

Just a program which can rename the files correctly, and makes B same as A...