All frameless cabinets are full overlay, the doors cover the whole front of the cabinet, framed comes in inset(most expensive), full overlay or partial overlay. Partial overlay is the most traditional looking and least expensive, and they look the oldest. I sell both kinds, but really prefer frameless because of the full access. If you have 3 drawers you have a board between each drawer that is unusable space. The drawers themselves are smaller in width because of the frame. Simple example, take a drawer from a 18" wide framed cabinet. That drawer will fit INSIDE the drawer in a 18" frameless cabinet. It is true you need a quality installer, but you should always get a good installer. Inexpensive cabinets installed well will look better over time then expensive cabinets installed poorly. Ask for examples of their work.

I address this question with our clients all the time. I sell more framed cabinets, because we offer more lines of framed, but personally I am a fan of both. I wrote an article about this, in the hopes that it would make the differences clearer to my clients:
http://cabinets4u.blogspot.com/2014/09/cabinets-101-framed-vs-frameless.html
I have sold both for years, and I think as long as you sell a quality product, the construction is less important.