I have owned and fired both SA and DA revolvers in .22 LR, .357 mag, and .44 mag. Most of my revolver shooting has been in the SA mode even when I'm using a DA revolver. This is especially true when shooting full power magnum loads.
The main advantages of a DA revolver are: (1) ease of reloading (2) variety of grip styles and sizes offered, (3) potentially faster followup shots, and (4) with some brands and designs, it's easier to quickly verify that the cylinder is completely empty.
There are no practical, structural, or design advantages inherent in the SA only revolver except one feature which is considered an advantage by some shooters: A heavy recoiling magnum with the traditional Colt Peacemaker style grip will allow the revolver to roll upwards and backward in your hand. Many shooters find this way of dealing with the heavy recoil of a magnum cartridge to be less painful and disruptive to their shooting. The other advantage to a SA revolver is cosmetic. The main reason most shooters buy them is because of their nostalgic association with the Old West, with Western movies (and TV shows), and with the sport of Cowboy Action Shooting. But there is virtually no important way in which SA revolvers excel over DA revolvers.
With some brands of revolvers, like Ruger, an SA revolver will weigh less and cost less than a DA revolver in the same caliber. But the difference is usually not significant enough to have much of an influence in deciding which revolver to purchase.
Years ago, a few old timers liked to claim that SA revolvers were simpler, stronger, more rugged, more accurate, or more reliable than DA revolvers. There was never any evidence to support these claims, although it may be true that most SA designs employ fewer parts than most DA designs. It is also true that some 19th century DA revolvers were more complicated, more fragile, and less reliable than their SA cousins.
But there is nothing inherent in the design of the best DA revolvers which makes them less strong, sturdy, or reliable than the best SA revolvers. The only reason that the SA design still survives is because of the nostalgia connection. That being true, the best modern SA revolvers use a sound design which makes them quite well adapted to the role of hunting and some styles of target competition. Their design disadvantages are relatively minor in these contexts, and SA revolvers often serve quite well in these roles.