CFC's were the first to be banned and are the ones that have been attributed with causing damage to the ozone layer. It was found that the chlorine atoms were the culprit. They were replaced with HCFC's(R-22 being one) which have a lower ozone depletion potential but still have a high potential as a greenhouse gas. HCFC's have been replaced with HFC's(R-134a, R-404a, R-410A). HFC's have almost zero ozone depletion potential but have a high greenhouse gas potential. Most HFC's have a higher greenhouse gas value than R-22. HFC's also take much longer to break down in the atmosphere than HCFC's so their greenhouse potential sticks around longer. Now there is a big push to replace HFC's with HC (hydrocarbon) refrigerants, R-290 is the most widely used and is what most manufacturers are shifting to as a replacement for R-134a. R-290 is a high grade of propane. It has been in use for a long time in specialty equipment but is now becoming the standard in consumer appliances and small systems with a small refrigerant charge and therefore explosion risk is minimal.
A big problem with HFC's is that many are zeotropic meaning the compounds within the blend have different boiling points(called glide) and different leak rates. If a system using a zeotropic refrigerant suffers a leak and only part of the charge is lost the remaining refrigerant must be recovered and sent off for destruction and virgin refrigerant must be used to recharge the system. If one "tops" off the charge the pressures and temperatures become skewed and the equipment will likely not operate correctly.
Another big problem with HFC's is the oil that is required. They use a very high grade of POE oil that is extremely sensitive to moisture. It also has a tendency to plate out forming a powdery substance that blocks capillary tubes and TXV's when exposed to high condensing temperatures. This usually burns the compressor up causing a piece of equipment to end up in the landfill. R-410a has the added problem of running very high discharge pressure. There are a lot of leak failures in R-410a equipment and all of the major manufacturers have had a hard time with ruptured coils. So, even though R-410a might be marginally better for the atmosphere much more of it is making it's way into the atmosphere due to leaking equipment because of the higher pressures.
I can say that equipment using CFC's and HCFC's seems to last longer with much less repair being required. Some of this may be due in part to the recent onslaught of cheaply built imported equipment but the inherent problems with HFC's definitely cause a lot more service problems than CFC's and HCFC's ever had. The question is, is the environment better off with refrigerants that are marginally better for the atmosphere but have inherent problems that cause a lot of equipment to be land filled prematurely due to failure? If you add in the energy and resources used to manufacture equipment to replace the large numbers that fail prematurely are HFC's really better for the environment?
It will be interesting to see how the HC's do. One advantage to the new HC refrigerants is that manufacturers can return to using mineral oil like CFC and HCFC systems and get away from POE oil and it's issues. I would like to see a lot more large scale systems going back to ammonia chiller systems as they are extremely efficient and ammonia being naturally occurring has near zero effect on the atmosphere.