The purpose is somewhat different than drogue shoot. Drogue shoot is for controlled falls, with reduced movement, but does nothing to prevent your eventual death. It is an instant tool that does not effect you for too long. Distress balloons temporarily negate falling at the expense of more movement, allowing you to keep gun arcs and rebuild your main balloon past one hit before it goes down again. Once activated, you have to deal with the effects for much longer, so much more strategy comes into play.
Like Zirilfer said, this is the Moonshine to Drogue Chute's Kerosene. Better benefits in certain circumstances, but more care needed when using.
In response to Crafeksterty:
The ship can still move, just more reduced than Drogue Chute.
About the same as a mine balloon. One heavy carro shot would take one out, I think.
It would help against them quite a bit, but if you take both you are leaving yourself open to a lot of other guns.
If you want to go for hull break, you keep firing at the main. The balloons 'pop' and can be redeployed every 60 seconds or so. This is ample time to carro any distress balloons and take out the main again. But while doing that, your foe will not go down. Concentrated carro fire will still take a ship running distress balloons down eventually, it would just take longer.
The time is guestimated at 60 seconds. Once you click to activate, you are stuck with the extra balloons for the next 60 seconds, whether you want them anymore or not. That is one of the drawbacks. Having these activated pretty much prevents you from going down at any effective speed. They would give you more lift, though. Combining them with hydro would make your ship rocket up... but then you are sorta stuck in place at the top of the map for the next 60 seconds due to added horizontal drag and inability to go down.
