Choosing frozen or live is mostly a matter of personal preference. Arguments can be made in both directions, and there are situations that specifically call for one or the other. Let's look at some universal principles first.
In either case, prey size is crucial. The prey you offer to your snake should be almost as large as the largest part of the snake's body. Compare the diameter of the mouse/rat to the diameter of the middle of your snake's body. If the prey is larger, you run the risk of injuring your snake.
Some handlers will tell you to move your Ball Python to an area separate from their enclosure to feed. Sometime in the past, the idea came about that if you never fed your snake in their enclosure, you would reduce the chances of being bitten when taking your snake out to be held. Please see a previous blog post on "Becoming a Snake Handler." The idea of moving your snake before and after feeding invites serious issues. For instance, when you feed your snake, you will likely not feed a completely filling meal. Ball Pythons are opportunistic feeders, and as such have the ability to consume relatively large meals. They do this to help them last during extended periods of not being able to find food. Instead, we feed frequent, smaller meals to sustain life and encourage healthy growth. Therefore, once you feed your Ball Python away from his/her enclosure, you must handle them to get them back into their enclosure. The Ball Python is likely still in "prey drive" mode, and would be more likely to bite you. In addition, handling your snake soon after feeding could potentially cause them to regurgitate, a possibly life-threatening incident.
Feeding your Ball Python in their enclosure is the best option for all parties involved. You will minimize your chance for getting bitten, and will reduce the probability of injuring your snake.
Frozen/Thawed rodents offer a convenience and safety factor that have made this option more popular. You head down to your local pet shop, buy a couple of months' worth of feeders and stock up. Thaw the rodent in warm water, and viola! Be sure to use tongs to present the recently-thawed rodent to your snake. Here is a video that illustrates the virtues of using tongs or hemostats!
Now that this example is out of the way, let's move forward. There are some downsides to feeding frozen that I would be remiss if I didn't mention. Recent confirmed salmonella and other zoonotic illnesses transmitted by frozen rodents have dissuaded some from using this option.
I personally feed live rodents to Ball Pythons. I find that my snakes respond to live feeders nicely, and I have a good source of rodents. I also do not mind watching my snakes kill their prey, which is a major issue for some. There are some considerations concerning feeding of live prey, though. Both mice and rats have the ability to kill your snake. That sounds odd, I am sure. I do a bit of snake rehabbing, and have seen the results of someone dropping a rodent into the enclosure with a snake and walking away. Disastrous does not even begin to describe the outcome. If feeding live, you must stay with your snake until he/she has successfully constricted and started eating the prey. You also must be prepared to take the rodent out if it begins to bite your snake. I have only encountered this on a couple of occasions, but it is a possibility. Your snake will not necessarily strike if a rat or mouse is attacking it. With those isolated issues aside, I still find it worthwhile to feed live prey.
There is a rash of vitamin supplements cropping up as of late, and I would like to forewarn you about these. The vitamin issues that send snakes to the vet are almost always overdose or overuse. In particular, Vitamin A can be very problematic for snakes in large quantities. If you are feeding a diet of rodents, your snake will receive all of the vitamins and minerals it needs, as nobody is running around in the wild misting all of the Ball Pythons with a supplement.
Never feed Gerbils to your Ball Python. If you start this trend, you will likely only be able to feed Gerbils for the remainder of your relationship with the snake.
I will address feeding issues in a later post, but if you have questions please comment below!