I haven't seen New order live, so I'll refrain from saying which band is better live. However, I've seen The Cure 3 times, and two of those shows are in my top three shows of all time. The last time I saw them was on the Bloodflowers tour, and they had to contend with playing most of Bloodflowers, plus the absence of Porl, so they weren't at their best.
Nevertheless, The Cure are one of the best, perhaps even the best, live bands, period. People here can hate Robert Smith all they want, but it's obvious from the effort they make in their live shows, in the regular release of material, etc., that The Cure really love their fans. From what I've read on NOOL, that isn't always apparent with New Order.
But, having said all that, I should also take this opportunity to thank New Order for heeding their fans' call for a proper tour this time around. They deserve the thanks of everyone on NOOL for listening and following through like that. 