What's the difference in these two methods of cabinet construction? Most people aren't aware that different types exist. I bet if they were made aware they would be more careful before remodeling their kitchen.
"Framed" cabinets, or "face frame" cabinets have a wooden frame around the cabinet opening. The hinges are mounted to the frame and a lip is created around the perimeter of the opening. There is often a center stile in between the doors of any double door cabinet. This used to be more of an American standard.
"Frameless" cabinets lack the wooden frame on the front of the cabinet box. The doors are a true full-overlay so you aren't looking at a lot of flat wood - You get more of the visual since the doors and drawers typically have the detail. You could say they are more sleek as the doors and drawers cover the entire cabinet box. There is not a frame to hinder the access of the interior like framed cabinets have so they are also called "full-access" cabinets. This also pertains to the drawers where you get more width than a traditional framed cabinet. Frameless cabinets also lack the center stile in between double door cabinets - This makes most people happy.
If there is one element of frameless cabinets that gives people pause it would be the edge banding which is often PVC. Even though the interior may be a maple or birch wood, the edge that sits behind the door is not. However, cabinets that are stained or painted on the inside to match the exterior (behind glass doors or in an open shelf unit) often have veneer edge banding for a better match. Inevitably there will be an area in your kitchen where the two types of edge banding come together - They may look a bit different - This is the main downside of frameless cabinetry. In my opinion, this is a trade off that is well worth it.
The cost difference is a bit of a gray area. Most cabinet dealers sell frameless cabinets for more money. This is where we disagree with most of the world - Assuming that they are both "all-wood" construction, frameless cabinets should cost less. There is simply less material, less wood in them. We do not charge more just because we can - Though they are more desirable. They are less money and, in our opinion, provide better storage and an overall better look.