In the cabinet business RTA doesn't mean IKEA-style particle board cabinets that screw together with camlock fittings. There are manufacturers that make cabinets for cabinet shops, who assemble them and install them. They also sell straight to the public. There are lots and lots of these manufacturers. Assembling these cabinets is like doing one third of the work of making your own -- you don't have to cut them or finish them, but you have to clamp and glue them.
I've done two projects with these kinds of cabinets. One was a simple kitchen, nine cabinets, six base and three wall, all stock sizes and colors, it was about $2300. At the other extreme I did a project that was 56 cabinets, a kitchen and three bathrooms, every cabinet was a custom size and a custom finish, that was about $44,000. On both projects for that money I got solid wood faces, plywood cabinets, solid wood drawers with dovetail joints and full extension slides.
Assembly is pretty straightforward. The pieces are precisely cut with dado joints and you glue them together. Hidden sides can be held together with a pneumatic stapler, sides that show need to be clamped until the glue dries.
I don't buy cabinets enough to know how the price compares. What I like about RTA is that they fit much better into my workflow. Cabinets are big and bulky and they're a pain to transport and store. I often work alone and it can take me a while to get them all installed, with RTA it's easier to set them out of the way and assemble them as I'm ready to install them. With a big bath double vanity it's much easier to carry the pieces up into the bathroom and assemble it there than to get the assembled cabinet up the stairs by myself.