Do you mean inset cabinets?

Inset cabinetry isn't appropriate for high humidity environments as the expanding and contracting of the wood could cause clearance issues in tight-tolerance inset cabinetry. If you have a whole-house humidity control system running year-round, then you'll be fine even if the outside environment is humid. Some of the less expensive lines of inset cabinetry like Shiloh's do not have as tight of tolerances as the higher-end companies that specialize in inset like Kennebec and Christopher Peacock. Bentwood and Plato Woodworking also have excellent inset cabinetry lines. You'll pay a premium for the better lines, and that means starting around the $1,000 per linear foot range. Is it worth it? It depends on your personal preferences and project budget. If this is a home you don't plan to be in long-term, your investment may not be as well spent with inset as something less expensive. Kitchen renovations rarely return 100% of investment at resale, and depending on all the factors, you return on investment could be far less than 100% if you sell in the near future.

This is a completely aesthetic decision so *worth* is totally a subjective decision based on your taste and budget.

Functionally inset cabinets can be LESS functional since they provide less interior space for drawers.

I recently finished a remodel and I do have inset cabinets on my upper cabinets but full overlay drawers on my lower cabinets. This is because inset cabinets in upper cabinets don't restrict space since you can tuck items behind the frames versus a drawer in which you lose the interior space. My combination looks quite nice.

I wanted a specific look especially since I ran my cabinets into the dining room area so I wanted them to resemble furniture and most furniture does have inset doors. My kitchen was also inspired by Arts & Crafts/Prairie which would have had inset doors. If I were going for a more modern look fully overlay doors would have not been aesthetically necessary.

Strictly for looks as far as worth it is concerned. If you have a very traditional style you might want to go with them but I much prefer full overlay.

Not just for looks. Inset cabinets can have butterfly hinges, which open 180 degrees. To my knowledge, overlay hinges do not open as far.

I love my Shiloh inset cabinets too. We wanted our cabinetry to look like furniture. We also have a run of tall overlay cabinets too. The inlay cabinets look more high-end in my opinion.

@catbuilder is correct. Overlay cabinets actually give you more storage space. Now, if space is not at a premium and you've got plenty of room for more cabinetry, then inset cabinets are lovely and clean-looking. They are more expensive, however.