Refinishing cabinets is one of the highest-return projects in a kitchen, and it's also the one most often recommended when it shouldn't be. The deciding factor is never the doors, which can be replaced on their own. It's the boxes.
Start by opening a door and looking at the box itself. Solid plywood or well-built particleboard that's square, dry, and firmly fastened is worth refinishing. Swollen bottoms under the sink, delaminating shelves, or a box that flexes when you pull on it all point the same way: the money is better spent on replacement.
Second, check the layout. Refinishing keeps every current decision in place: where the pantry is, how deep the corner cabinet reaches, how far the counter runs. If the reason you dislike the kitchen is the layout rather than the color, no finish will fix it.
Third, look at the door style and the material. Solid wood and MDF doors take paint beautifully when they're cleaned, deglossed, and primed properly. Thermofoil that's peeling and laminate over particleboard are much harder to get a lasting finish on, and that's worth knowing before anyone quotes it as a simple repaint.
Fourth, be realistic about the process. Done properly, refinishing means removing doors and hardware, cleaning off years of cooking residue, sanding or deglossing every surface, priming with a bonding primer, and applying a finish built for cabinetry. A crew that quotes it as a one-day scuff and roll is quoting a finish that will chip at the handles within a year.
When the boxes are sound and the layout works, refinishing gets you most of the visual result of a new kitchen for a fraction of the cost. When they're not, paint just delays the real project.