What are the best acrylic resins to make dentures, or does each dentist have his own favorite?

No best and no. Resins used to make dentures are very generic as to materials very little in composition. It is sad that dentists try to use the material in the denture base to differentiate a cheap versus a deluxe denture. The expense to the dentist from the lab for a customize base resin is small and can lead to deception in its cost. Yet, adding blanching, pigment and fiber can improve cosmetics. Be aware.
Variable. Some differences. Most popular and longest used material is methylmethacrylete. There are other resin materials, depending on the denture requirements. New developments continue. I have been doing this over 30 years and i prefer the methylmethacrylate.
Many good choices. Lucitone 199 used to be the choice for many dentists ordering denture fabrication for patients. While I do not know current brand names, there are may good companies producing great acrylics for dentures like dentsply, ivoclar, 3m, etc. Each acrylic resin has its own strengths/weaknesses. Most that are durable are heat cured however.