I use rechargables and brightness isn't a problem. I just charge them once a week so the voltage never gets very low. I can't really tell the difference between a fresh alkaline battery and a week-old rechargable.
Newer rechargables also have much less problem with self-discharge. I've even started using them in remotes without any problem. I do still use alkalines in clocks, but they will generally run a year or more on a half-dead battery. I know because I get my alkalines out of the battery disposal bin at work; lots of people mix new and old batteries in a device, then when it stops working they throw away the lot, but there wind up being a lot of practically new batteries in that bin.
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Work: the 8 hours that separates bike rides.