Great question!
Simply these are 2 different ways of constructing a cabinet!
1) A framed cabinet has a rectangular “picture frame” in the front. The doors hang on the frame, to the outside. The cabinet box is connected to the frame on the inside, often set in a routed-out grove. The frame keeps the box square, so all the corners are exactly 90 degrees.
A frameless cabinet generally requires thicker side walls than a framed cabinet and needs a system like corner brackets and/or stretchers to maintain the cabinet in square.
2) Euro style cabinets i.e. flat panel doors, are almost always frameless.
Most of the traditional cabinet styles had picture frame doors, hung on a framed cabinet. That door whether rectangular or arched, had an inserted or central panel. That panel could be flat, raised with a routed pattern or glass.
Today you can find many traditional door styles on frameless cabinets as well.
3) I think a major consideration to your choice of Framed vs. Frameless is how level are your floors? If your floors are not level, a framed cabinet is much easier to install and maintain its original square shape.
Framed cabinet doors have 1/4″-1/2″ reveal of the frame.
Frameless cabinet doors have no reveal and must cover the entire box.
4) As noted, Frameless cabinets are heavier both in the base and the wall cabinets as they utilize 3/4″ or even 7/8″ lumber vs.. 3/8″-1/2″ for framed.
Frameless also require hinges with greater flexibility & range of motion than framed cabinets, to allow you to square the door with the frame.
5) Most framed cabinets come with their side panels finished, whereas most frameless cabinets come with their side panels unfinished, they therefore require additional finished side panels.
You must add the cost and extra width of these side panels to your calculations.
6) Almost all cabinet boxes are constructed with plywood, a series of thin wood layers wherein the sides are nicely finished and can be painted, stained or laminated. However, the plywood ends are rough!
Framed cabinets bury these ends into the routed frame grove and are never seen from the front.
Frameless cabinets ends are seen with the door open, hence they usually apply a plastic edging film to cover the plywood ends.
Framed vs. Frameless is a factor that should be considered along with other cabinet features.
Ultimately however, I think consumers will choose their cabinet based on major factors like color, style, manufacture, availability and price.
Your decorator, designer, distributor and contractor will have a significant influence on that final decision.