New Order by a comfortable margin, though I do like the Cure. Kind of surprised you didn't go with the Smiths on brooding Brit bands, but okay.
Gotta go with the Cure on this one. After all, Robert Smith was immortalized in an episode of South Park. Vanquishing Mecha-Streisand has to count for something.
New Order based solely on the "Ceremony/In A Lonely Place" 12". Oh, I like some Cure fine, they put out some good pop tunes, but the crap/good stuff ratio is much higher for Mr. Sumner & Co than for Mr. Smith & Co.
New Order, based on the secondary Peter Hook vs Simon Gallup battle, which is a close one. Hooky's pretty cool.
amen, brudda! Echo and the Bunnymen hands down over these two. The Cure more brooding than New Order, though. well, more "whiny goth inspiration music" than new order in my experience.
In the battle of the brooding Brit bands, New Order's Everything's Gone Green is by far the best song produced by either band. Not that I don't like The Cure.