Ulysses
I am not sure if you are running Tiny Core from a usb drive, or a hard drive.
If you are running it from a usb drive, or other solid state memory, using backup will prolong the life of the drive.
If you are running Tiny Core from a hard drive, you are better off with persistent home and opt. Any difference in performance will only be fractions of a second. You will not notice it. The only thing you will notice is the time taken to start up and shut down when using backup.
I was never concerned about the time taken to shut down. You can shut down Tiny Core and walk out of the room. After backup is complete, the computer will be turned off.
What annoyed me, was the time taken to start up. You want to be able to turn the computer on and use it. Not turn it on, and wait and wait and wait.
I have not used backup for a long time. I use persistent home and opt, and make new extensions for personal settings.