Via using the dynamic_sidebar() you can change/edit the widgets in the widgets area of the appearance settings. If you use the_widget() you hard code it straight to template so you need to modify the code to change what is displayed.
Both have their uses. Too many sidebars tend to clutter the widgets area, but is very good for users that don't want to mess with the code (or if you swap around widgets/widget settings often).
The_widget isn't dependent on having a sidebar so it has it's uses too if you have a lot of custom widgets that you use around your templates, like in the footer for example.
But I don't think there are straight up benefits of using one vs the other, other than usability wise.