Box cabinets come in widths of 3 inch increments (12″, 15″, 18″, 21, 24, etc.) this means if your cabinet length is 5’ 2 1/2” you will need a 2 1/2” filler section on the facing of your cabinets. Custom cabinets are custom fit with no filler sections and more useable storage.
With box cabinets you have face frame of 1 1/2” wide per box, when you join 2 boxes together it becomes 3” wide with a vertical seam between all the boxes. Custom cabinets have face frame of 1 1/2” –2” wide allowing more room for access as well as wider drawers.
Most box cabinets have a 1/8”-1/4” overhang on the face from the cabinet box. This makes it hard to put crown molding around the top of the cabinet, as well as toe shoe around the base cabinet. These box cabinets have no extra material to custom fit the boxes to the wall. There will be a gap between the back wall and the cabinet. If the person installing the cabinet followed the bow of the wall now the front face of the cabinets are no longer straight. Installing a counter top on these boxes will have to custom made to get a big enough overhang on the counter top to make it look good. If there is a bow in the wall this could be hidden with custom cabinets.
The only time a box cabinet looks above average is when it has a full over lay door covering most of the face frame.
All the quality in box cabinets is located in the appearance of the cabinet, not in the operation, structure, or functionality.