A great overview on the difference in behavior, but I don’t think it answered OP’s query:
I’ll split the two, but here are the applications:
If your application requires full or nearly full force in both directions, use double-acting cylinders. If it requires significantly higher force in one direction than the other, consider single-acting cylinders, with the action being in the direction requiring the larger force. Doing this can save a lot of air. Another consideration is what happens if your pneumatic system springs a major leak; a single acting cylinder will have a well-defined action; if you’re big on fail-safe, single action may be the way to go, even if it means providing more return spring than the cylinder provides.
Note also that a double-acting cylinder can be used as a single-acting cylinder with the addition of an external spring or counter-weight. This isn’t the neatest solution for today’s problem, but it may be a better use of funding when considering re-use of components (I have absolutely done this, and would do so again, as that cylinder from 2016 was re-used in the 2018 post-season to great effect!).
If your device spends most of its time in one state, a single solenoid valve is likely a good fit. You will only need to provide current for the “unusual” state. If your device spends roughly equal times in each state, especially if the transitions are more than a very few seconds apart, a double solenoid valve is likely the right answer. (Just make sure that the solenoid is turned off after the transition has taken place!) Not as big a deal today as before the PCM, but there is always the limitation of how many pneumatics channels you are using that may push you to single solenoid valves.
On the crossover, if using a double-acting cylinder, a five port solenoid valve is required (or two three port valves, but one of them is likely to be misused in this case). If using a single-acting cylinder, a three-port solenoid is adequate, but I’d rather order a five port solenoid and plug the extra holes because it’s more likely to be useful in a future year.