Randy, yes they both have the same LED but the ciruitry is entirely different. The LS uses an electronic regulated circuit that provides a constant current source to the LED thruout the useful life of the batteries. The Reactor is "direct drive" meaning it is driven straight from the batteries. In all liklihood, the Arc LS will be brighter initially and certainly will maintain the level of brightness for a longer time then the Reactor. As other's have posted the Reactor does much better with lithium AA's then alkalines as the initial voltage is higher and the discharge rate is flatter.
From personal experience my Reactor on alkalines is noticably dimmer then my Arc LS. The Reactor on lithiums is just slightly dimmer then the LS but will maintain the brightness longer then the Arc LS. Having said that, I would much rather have the Arc LS.