Again, for Migration Assistant, a fairly reliable method is to make a Time Machine (or clone-type) backup on an external drive. Then run Migration Assistant on the new Mac and when prompted, connect the backup drive to it and tell it to migrate only the user account(s) and files, nothing else (no settings, no applications ...). You never have to connect the two computers or run programs on both together.
I recently did this on a new Mac running Catalina, migrating from one on High Sierra. Worked very smoothly. High Sierra is more recent than El Capitan, of course, but migrating only files should work fine. Install applications anew on the new Mac, being careful to use only the latest installers, check online first before each install for compatibility with the later MacOS, and avoiding installing any anti-virus, security packages, or "cleaner" programs.