There's so much to talk about, so this is a work in progress but we assure you, we're working on it.
So your asking which is better?
Ultimately, there is no right or wrong. Some people argue the Frame adds rigidity to the front of the cabinet where the openings are, so in theory where the cabinet would be weaker. However, most of the time cabinet manufacturers will use a heavier duty material on frameless cabinets to make sure they stand up. If its a cabinet from The Norfolk Kitchen Company, you DO NOT have to worry about durability.
Which is better value?
In my experience, Frameless is better value, it provides ever so slightly more usable storage space, they're normally easier to install, and if you ever get sick of them, they're a lot easier to reface.