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large bandwidth gives you a fast dynamic response that can gives you more tolerance for dynamic changes but the stability could become an issue.
small bandwidth is usually more stable but due to the slow response the circuit may not be able to respond quickly to changes in the load current so you will get larger spikes in voltage due to step changes in the load current.
So it is a compromise and it depends basically on the specification you have for the circuit.
Yes, as fahmy pointed out you need a high BW for better transient response. At the same time , you should not compromise on your gain as a good gain improved tracking the feedback better . For a a test try giving a current pulse from min to max with a very steep rise/fall time and see your droop in the output voltage of the transient response . If its dipping very low one major effect could be because of the slewing . So , a higher current ( read bandwidth) will solve your issue .
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