All manufacturers I know of make face frames from 3/4" solid wood. You will occasionally find 1" available from higher end companies, most often for aesthetic reasons not for strength.

How the frame is made? This is more definitive of quality than almost anything else that you can easily find out about. Less expensive brands will use pocket holes and screws to join the frames. Next up are doweled frames. At the top end there are true mortise and tenon. A few mid range companies offer loose tenons or a variation on dowels. That sounds nice but in my experience the results are not done as well as doweled cabinets.

How are the boxes kept square? Plastic corner reinforcements, wooden corners (better), full plywood struts along each side (even better), and finally at the top end full sub tops or dust tops. Inset cabinets should always have full dust tops in my opinion.

Sides- How are the sides joined to the cabinet and what are they? First off what are they? (note particle board will often be called furntiture board, long grain flakeboard, and occasionally incorrectly MDF. Of the 500 or so mfgs out there only a handful actually use MDF for boxes) Cheapest will be 3/8" particle board, that is a case wherer you should upgrade to ply. Then comes plywood-3/8". 1/2" for standard sides are common- 3/4" for standard sides is not common but can be found at local custom makers. It keeps customers happy and is easy for them to just buy it. It is unnecessary in a framed cabinet.
3/4" (or 5/8") is more common in flush finished sides and desireable. There is often debate over plywood versus particle board. I find nothing wrong with particle (especially for frameless) depending on what it is, some of the plywood used is simply no better. But a lot of folks will argue this.
How good the particle or (ply for that matter)is will vary. If looking at manufactured cabinets I would go more by price/reputation than worrying about the specifics. It is unlikely that the salesman can answer with authority what type, where it came from, what grade, etc. When I'm looking for a mfg the reps usually have to put me in touch with the factory to get those answers. Local shops are less likely to use particle. Domestic or Canadian particle or ply is better than Mexican (particle) or Chinese (any)

More importantly is how the sides are joined to the box. Most of that you can only tell by looking at an uninstalled cabinet. Best are into dadoes and glued, staples are ok if the glue is done properly and the fit is tight. Lots of staples is a bad sign. A little glue exposed is a good sign. I would rather see some glue that was not cleaned up than get a glue starved joint.

Almost everyone will give you dovetail drawers. There are other constructions used by local shops and often are fine and will still last 30 years. 1/2" box sides require better wood than 3/4" sides. I will not sell a cabnet with Chinese drawer glides- I only consider Grass/Mepla, Blum, KV or Accuride glides. (in that order for undermount)

What type of finish- full conversion varnish is arguably the best but nothing wrong with pre-catalyzed varnishes used by local shops. How much is used and how well it is applied matters more. Almost no one can tell you what the "wet build" is for the finish on their cabinets. (you should see the look on reps faces when I ask that :) Run your hand along the bottom edges of drawer faces- feel smooth and consistant- good. Best way to tell finish.

Warranty- mfgs will give you a "limited lifetime warranty" This is a great marketing tool. If you are going to have a defect it will be in the first year, after that everything is wear and tear. So you are then left to the good graces of the mfg. Better mfg will take care of things forever as a courtesy, cheaper ones will be less likely to do so. Hardware is almost always for life and not usually difficult to bet taken care of.
What "grade" of wood is used for doors AND what they consider a replaceable door. If you are getting light colored woods you want a better grade of cabinet if you are fussy. Some manufacturers will replace a door if the salesperson asks, others require it be warped a specific amount (as much as a 1/4") some want it to acclimatize for a year, some have a size limit on doors for warranty.