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 .