Good oil based floor paints are urethane reinforced and water based ones are epoxy reinforced. Benjamin Moore makes the consumer market type coating I know best but SW and others have similar products.
Sort of the next step up are two part liquid epoxy coatings. Abatron makes a great product. You can add speckles and stuff. Frankly, if you are going to head this direction get an estimate from a company that sprays the epoxy on from a truck that mixes parts A&B to the exact proportions without air bubbles and at just the right temperature. The Accura dealer I used to take me care to for service had a sparkling white floor I thought really dangerous for a service department but in the years I had the car it always looks spectacular.
All the major paint companies have industrial coatings divisions and sometimes marine finishes are also worth considering. Specialty companies like US Coatings and US Coating Solutions make newer chemically resistant and nano-technology cement floor coatings and silicon reinforced products. For a price.
Almost as important as what you choose for a coating is the prep ahead of you. You need to get all the peeling paint off, if not all the paint, and make the floor spotless of grease and anything that will interfere with adhesion. You may have to etch it for adhesion.