I've never experienced a problem with stalled horses, even during many years at large show training barns of up to 150 stalls - if properly managed, most stalled horses will fare absolutely fine. If improperly managed, even horses turned out 24/7 can experience issues. There is no one best option across the board, it has to be what's best for the individual horse.
When I bought my horse, I boarded him in a paddock w/3 sided shed so his 20 month old body had the option for constant movement. He was MISERABLE when fly season hit, covered in welts, blisters, and rubbing himself raw from itching no matter what fly control methods I tried, even though the other paddocked horses were fine. Once it hit 100°F, he also started with excessive sweating and a constantly elevated respiration rate, so I moved him to stall board. A year and a half later, he still gets turned out 16 hours a day in the Texas summer, but spends the hottest part of each day in a stall under a fan. He's happy as a clam and super healthy! During the winter, he's in the barn if it's below 30°F (a rarity in Dallas) or raining/snowing/muddy/icy, but otherwise turned out and still happy as can be.