Moving caged hostiles invariably results in their escape, in my experience.
Once your dwarves have some experience, anytime you get the "snatcher! protect the children!" warning, you can draft the nearest dwarf. If he's Legendary, or even close, he's likely more than tough, strong, and agile enough to beat the f**** baby snatching bastard to death with his bare hands. This is immensely satisfying and I recommend it. Even if the dwarf dies, he dies a hero!
And with a miner or woodcutter, I can recommend this even for ambushes, I've seen woodcutters and miners destroy entire squads of goblins without any injury.
Moving caged hostiles does not always result in attempted escapes, thieves of both goblin and kobold variety will almost always try if they are let out to be pitted. However, my own experiments have shown this can be reduces by stationing active military nearby, it seems the presence of a military dwarf is one of many factors.
Caged invaders from sieges and ambushes escaped a 30% of time when I tried without military nearby, it was reduced to 1 in 5(20%) when I stationed a few recruits near the cages. The ones that did escape had their parts decorating the floor.
Thieves had now been reduced to maybe 60% attempted escape, a small improvement, but overall not good for the goblin's health.
This has been done with 10 tested goblins from invaders, and 5 thieves for each of the situations. Large scale testing may be needed to confirm this or improve the results and/or theories.