Is outdoor exercise in good conditions (ie. not raining, not super hot, no snow) better for you than exercising indoors? Many people exercise outside for fresh air, but does it only feel good or is it also good for you?
It's certainly more interesting running outside. Treadmill running (or wind training cycling) is very boring and takes a lot of mental toughness to complete. Running outside with friends is far more interesting. Certainly, I find that running on trails is something that makes me happy.
That's a very personal answer which doesn't answer your specific questions. If you enjoy your exercise then you're more likely to do more of it; that's your benefit.
One meaningful difference between exercising indoors and outdoors is the oxygen content of the air around you. Oxygen content tends to be lower indoors, simply because of the buildup of CO2 and other gases which compete with oxygen.
How strong the difference in oxygen content really is depends on the ventilation system of your indoors environment. If you have great ventilation, there is virtually no difference between indoors and outdoors, and the exercise will be the same for your body. If the ventilation is poor, exercising indoors will have a similar effect to exercising at a higher altitude level, which will lower your endurance. The oxygen difference might decrease your performance to some degree, but it shouldn't have negative consequences for the desired training effect, whether it's conditioning or fat loss.
Of course there are other differences when you compare the specific type of exercise you're doing, e.g. running on a treadmill is different from running in the woods. Running in the woods requires you to change directions, run at different angles, avoid obstacles, etc. which will involve different muscles than running on a treadmill. On the other hand, running on a treadmill might carry a smaller risk of injury. So in addition to the oxygen issue, you have to consider exercise-specific differences.