New drive + new OS, but will Time Machine restore old OS?
Using Migration Assistant is the same as restoring from a Time Machine backup. Restore data from your Time Machine backup will not change the version of OS X that you are running (i.e. you will remain at OS X 10.11 regardless of the version of OS X that created the backup).

You lose none of your information or metadata. You will not restore any system files, but all other files from your backup will be restored, including but not limited to files you created and saved, along with their metadata (date modified, etc).