I've only used bands. Never chains. So I haven't voted.
We bought bands because they were cheaper and more convenient. They fit in a gym bag.
I liked bands for Speed Squat work when using the basic westside template. Bands do something I think is valuable on the eccentric portion of the Squat: They make it difficult to descend under control and remain stable. This is real "core" training. Much better than stupid exercises performed on a Swiss ball. Regarding the concentric portion of the lift, they are, of course, very valuable for teaching you to drive the bar from the hole through lockout.
I would probably also use them to assist with pull ups so I could do really high reps. I think bands have a ton of uses. Get creative with them.
Two caveats: I used bands when doing BOX SQUATS on speed days. I don't know how they would work if you were doing free-squats, either paused or with the stretch reflex.
Second, I found it very easy to end up with too much tension on the bar. Speed days invariably ended up being max effort work. We just underestimated how much band tension there was, and next thing you knew, you were working up to heavy-ass doubles. That wasn't smart.