Frameless cabinets are usually doweled together with a dadoed back and the hanging rail is either doweled or glued and pinned. For the most part, the hinge on a frameless cabinet is better than one on a framed cabinet. The hinges have more adjustments than most and they unclip off the cabinet without unscrewing a thing! Installers like them because of their ease of installation. A frameless cabinet also gives you about 15% more cabinet space because of the way it’s constructed.
According to most things on the Internet, framed cabinets are stronger than frameless because the frame supports the surrounding box. It’s hard to dispute since most of us grew up with the framed cabinets from the last century. While certain things such as finish and drawers have improved, sometimes-questionable parts (substitutes) have been used.
Door quality is highly important. For most companies, the doors are a high percentage of the price of the cabinet. The amount of moisture left in the wood after the curing process, the size of the planks of wood used for the panels in the door, the quality of the wood and how the pieces are joined are all part of what makes a good door. Having the finish put on after the stain and having the stain put on by hand instead of automatically, really affect how the door looks when completed. With a painted finish, the quality of the wood and how well it is sanded, really make a difference. Paint quality has a lot to do with it and catalyzed finishes are a must!
Hinge and drawer guide quality are equally important to look at. With so many knock-offs out there, it can be difficult to find good hinges and guides. Look for name brands on the parts.
Finally, the way the cabinets are packaged and shipped can make or break the cabinet you have chosen. Many boxed cabinets are not treated so nicely when being shipped. Choosing a company that ships their product with their own trucks helps a lot.
Hope this helps!