Frameless cabinets are often referred to as EURO or Full-Overlay. If you look closely at the image above, you'll see the front edge of the cabinet box, is actually just a finished edge on one of the boxes panels. The gaps between the doors and drawers is minimal, leaving very little of the box exposed, this is why its called Full-Overlay.
FRAMED or FRAMELESS?
So you are wondering which is better?
Ultimately, there is no right or wrong answer. Some people argue the frameless adds rigidity to the front of the cabinet where the openings are, so in theory the cabinet would be weaker.
However, most cabinet manufacturers will use a heavier duty material on frameless cabinets to make sure they stand up.
If its a cabinet from The Norfolk Kitchen Company, you DO NOT have to worry about durability.
Which is better value?
In my experience, Frameless is better value, it provides ever so slightly more usable storage space, they're normally easier to install, and when you are ready to change up your kitchen style, they're a lot easier to reface.
Framed cabinets are the original North American way of doing things, sometime called partial-overlay. If you look at the picture below, you can see how the front face of the cabinet has sort of a picture frame around the perimeter and between the openings. So the frame is separate from the panels making up the box of the cabinet. The gaps between door and drawers is also larger.
Refacing is perfect if your current kitchen layout meets your needs.
Refacing allows you to keep your cabinet boxes but upgrade your cabinet doors and hardware.
Refacing usually gives you the look of new cabinets for about half the cost of new custom cabinets.