The books solution, is definitely cleaner, and the biggest difference I can see is the books solution is actually sorting the variables, rather than just changing the display order.
In terms of efficiency, displaying stuff to the console is more efficient than popping up message boxes. There's less conditional logic in the books solution and a lot less code duplication. Other than that, there is very little difference in the sorting operation, the books maybe slightly more efficient due to less conditional checks.
Overall though, in my opinion the book provides the better solution, because it has virtually no duplicated code, conditionals are a single level deep (much easier to read), actually sorts the numbers in memory (if this program were to do more, your variables would already be sorted for you next time you need them, as opposed to having to duplicate the conditional logic, and overall it's much easier to understand what it's doing and what's going on.