Like you said, the main benefit is control. I'd say the two main variables you're controlling for are amount of fat in the mixture and the tenderness and quality of the cuts used. Depending on the application, you might use a different mixture of meat. (For burgers, Alton Brown uses a 50/50 mixture of chuck and sirloin.)
Grinding your own could also be considered a play for increased food safety. If there are any bacteria on the surface of the cuts of beef that go into the grinder, they will be pretty well distributed throughout grind. The longer (and warmer) the ground beef is stored between when it is ground and cooked, the more chance that the bacteria could grow to sufficient numbers that they could do some serious harm to the consumer. This is why it's recommended that ground beef is cooked to a higher internal temperature than say a steak. In grinding, everything effectively becomes surface area so you have to cook a burger all the way through to be sure you've killed any bacteria.
If you're grinding you're own, you can make the interval between grinding and cooking arbitrarily short, so if you want to take your chances with a rare burger, this would probably be the best reason to grind your own. You're still running a risk in this case as any bacteria that were on the outside of your meat are now on the inside of your burger and won't be killed if the meat is left rare. You would just be trusting that the butcher did a good job of keeping the outside of the cuts you purchased relatively free from infection. Also, any food safety benefit assumes you're doing a good job of cleaning your equipment. Meat grinders can be a real PITA to clean well.
As far as the flavor difference is concerned, I would assume that to be minimal, again if you control for any difference in quality and cuts of beef that might be used. If your butcher grinds the beef and stores it cold in a case or wrapped for a day or two before it goes out the door the flavor shouldn't change enough that you'd notice it after seasoning and cooking. Oxydation would have had a chance to change the color of the meat over that period, the reason why ground beef can look brown on the outside but still nice and pink when broken up. But there shouldn't be enough time for there to have a marked effect on the flavor.
If there is any perceptible flavor difference you'd probably notice it more in a burger where you're tasting the meat by itself for the most part than in something like a chili or stew. (As an aside, you don't necessarily need to grind all the meat in those anyway as they tend to be cooked long enough to soften bigger chunks of tougher cuts.)
Yes, fast chilling is critical because it minimizes the production of new bacteria and potentially deadly toxins from the spores of anaerobic pathogens such as C. botulinum and C. perfringens. The spores are not killed by the low temperatures usual in sous vide, and the oxygen-free environment of the bag brings them back to activity. But they require time and temperature to become active and dangerous, so fast chilling -- either refrigeration or freezing -- and limiting the refrigeration time (to about 5 days at around 5°C/40°F, longer for lower temperatures) are absolutely critical to deter them.
The question starts with a situation that is different: cooking in an oven, which is not an anaerobic environment and thus does not trigger the same activation of the spores' lifecycles as cooking in a vacuum does.
Best Answer
I will disagree with the other answer for one simple reason -- the fewer steps taken en masse, the lower the risk.
Now of course, this assumes that you're correctly cleaning your grinder, but because you're only grinding one chunk, or maybe a few chunks of meat, you only have to worry if those chunks of meat had contamination.
For a larger operation, every piece of meat that came before it since the grinder was last thoroughly cleaned could possibly contaminate the ground meat that you've purchased.
This of course assumes that the large cut of meat hasn't already been infected because of the butchering or some other earlier processing step. (such as if many butchers are then feeding into a single grinder).
Now, is the change in risk enough to worry about? Probably not, but it exists, however slightly. If you want to be really paranoid, sear the outside of a roast, then trim them off, then grind what's left. But of course, if your grinder isn't sterile, you're just shooting yourself in the foot.