Rent both. Then buy the DC
I vastly prefer the director's cut (which Stone calls the "10 month cut," as opposed to the 7 month theatrical), for its thematic clarity, eliminaton of redundant and/or unnecessary moments, and sharper editing and pacing. The decision to juxtapose his young life with this adult life in the 10 month version (this was how it actually was in the original script, the move to an all linear plot for the theatrical release was a last minute decision for the sake of coherence) makes for a much stronger dramatic arc, and offers for some powerful punches in the last 2 acts of the film; also, this move avoids frontloading by keeping Val Kilmer and Jolie in the entire movie, as opposed to just the first act. It also makes the cut to Philip's assassination less jarring, as the whole film is intercut. Structurally it is quite similar to Oliver Stone's (masterpiece) Nixon, which intercuts Nixon's childhood with his presidency. Also, the Indian battle seems to be even more ferocious on the DC; I suspect that it's been srpuced up, not unlike the LOTR: EE's. It should be noted that the DC is not merely a reshuffling of scenes; MOST of the scenes in the film are either subtly or dramatically altered, whether it be a few snippets added here, a couple seconds dropped there, a shot cut away a little sonner, or an alternate take. The refinements are pervasive, both large and small. Editing enthusiasts like myself should have a field day. Here is one of my megaposts concerning the new version of Alexander -
http://www.hometheaterforum.com/htfo...46#post2752746
I suggest going through that whole thread, as there are a number of intelligently articulated (and wildly differing) views on the film that will hopefully help you make your decision.
Regards,
Nathan