rechargeable battery. as in the USB type that's all built in.
Love my CYGOLITE 350. Got it on sale for like $45 last year. I've also got a SERFAS 200. I think I halved the battery life by running the light with a 10,000 mAh pack plugged into it. When I would ride in cold weather, the battery would not last long (as expected). So I'd carry a cell-phone sized battery pack to plug into it.
For tail lights I have both, USB rechargeable and replaceable battery. I go cheap on tail lights since you don't know until you get where you're going if you lost one.