The picture on the right represents the stronger design, in my opinion. In the picture on the left, there's nothing that supports the "glue block" that everything is attached to. The entire weight of the cabinet is resting on that small block! It wouldn't surprise me if it had a great tendency to separate from the base of the cabinet.
I'd go with the diagram on the right, but I'd make one small change: run screws into both the glue block and the base. Stagger them so they don't interfere with each other. Of course, if you're working with wood you want to use both glue and screws to secure everything.
FWIW, an inexperienced woodworker will probably find both designs difficult to execute. The base must match the cabinet dimensions pretty accurately in order for the design to work. That means that all of the corner angles have to match as well as the lengths and widths of the base.