Cabinet painting is one of the highest-return projects in a house, and one of the easiest to do badly. Done right it changes the whole room for a fraction of a replacement. Done in a weekend with a brush and wall paint, it stays tacky, chips at every fingertip, and looks worse than what you started with.
The first question is the boxes, not the doors. If the cabinet boxes are solid — plywood or well-built particle board, square, with drawers that still run true and hinges that hold — refinishing is almost always the better value. If the boxes are swollen from a leak, sagging, or falling apart at the joints, paint is money spent on a structure that's already finished.
The second question is the layout. Painting keeps your kitchen exactly as it is. If the real problem is that the layout doesn't work, no finish fixes that, and refinishing just delays the decision.
The third question is the door material. Solid wood and MDF doors take a finish beautifully. Thermofoil and laminate need specific bonding primers and careful handling, and some are honestly better replaced — a good painter will tell you which yours are before quoting.
A proper refinish is not a quick job. Doors and drawer fronts come off and get labeled. Everything is degreased thoroughly, because kitchen grease is the number one cause of adhesion failure. Surfaces are sanded, bonding primer goes on, then two finish coats of a cabinet-grade enamel that cures hard rather than staying soft.
Then the doors need to cure before they go back on the boxes and before anything is stacked against them. Rushing that step is why so many painted cabinets show fingerprints at the pulls a month later. We'd rather leave your doors off two extra days than hand back a finish that won't survive the first Thanksgiving.