The manual you linked describes the enhancements BOS advertises in comparison to SOS, see page 5:
Thank you for purchasing this copy of BOS - Bob's Operating System for the Apple ///. It has been designed to help you use your Apple /// more effectively by bringing some of the features of the newer style computers to the venerable old Apple ///. BOS provides a built-in program switcher, disk caching, print spooling, a screen saver, automatic uncopyprotection of Apple Writer, VisiCalc and Advanced VisiCalc, startup and individual program password protection and allows you to set a program to automatically run upon booting up your Apple ///.
• If you are familiar with Selector or Catalyst the BOS Program Switcher will seem familiar yet more powerful than what you're used to. A program switcher lets you place your programs on a hard disk (or large capacity floppy) and switch from one to another by selecting it from a menu, without restarting your computer each time or typing in complex program pathnames.
• Disk caching allows you to set aside a portion of your Apple ///'s memory to use to hold frequently accessed disk information. This dramatically speeds up access to your hard disk and slows wear and tear on your disk drive. Since many programs frequently access the disk drive, your programs will appear faster because it takes much less time to retrieve information from the cache than from the disk drive.
• Print spooling sends information to be printed to a temporary file on your hard disk and sends the information to your printer in the background. This allows you to use your computer while it is printing something, letting you do more in less time.
• BOS has a built-in screen blanker which can turn your Apple /// monitor screen off to prevent phosphor burn-in which can leave shadows on your screen. The BOS Blanker can also show a variety of soothing patterns and with the optional BOS Blanker Pack you can have sophisticated displays at a variety of times or on your command.
• BOS provides automatic uncopyprotection of AppleWriter, VisiCalc and Advanced VisiCalc, removing the need for the .UNCOPYPROTECT driver.
• BOS provides security for your Apple /// by giving you the ability to set a startup password that must be typed in upon starting up your Apple ///. Additionally, you can have BOS ask for passwords on specific (or all) programs so you can prevent unauthorized use of your Apple /// and the programs on your hard disk.
• BOS is fully compatible with programs requiring SOS 1.3 and SOS 1.3(S). It works with the Desktop Manager and other popular programs designed for the Apple ///.
• BOS has improved memory management routines to make available more memory for many of your programs. In some instances, up to 31.75K more memory than Selector or Catalyst
If someone wants to inspect the actual software, disk images are available here
