Field, some horses especially competition horses get stressed out in a stall
Field - space to stretch and just be a horse in their natural space !
My horse does competition and he’s kept in a field. At night he’s kept in a small paddock as his diet is different than the other horses, but the rest of the day he’s let into a large field to run, graze, and spend time with other horses. It keeps him much happier and his demeanor more pleasing.
They are horses so 100% in a field. Horses need to run and play not be keeped in a wooden box :)
In a stable, but also let walk out for a few hours
There are advantages and drawbacks in both situations.
-advantages: the horse has a better mental health as it is his natural way of living, they keep their muscle structure as they are walking (or cantering sometimes ahah) all day long, it is very good for horses who have a lot of energy because they can exert themselves somewhere else than when they're being ride ;)
-drawbacks: he can have problems such as pulling the shoe or others if he doesn't go along with the others horses in the field (always shoe the two fore), it is also more complicate to look at what he's eating and can gain weight. If your horse is used to go to the field he won't go crazy (as some horses do because they never go) and so there are less risks of injuries.
-advantages: ideal for young horses so that they have more link with humans and get used to their company, for old ones too because with cold for example they can get osteoarthritis, there are also less mud problems.
-drawbacks: it is very small and the horse gets bored (he can turn in circle or even develop stable vice.
Finally we can ask ourselves if it's not an advantage for us (riders) more than for the horse to be in the stable?
I hope i could answer your question :)