Hmmmmm.
Of course, Pop (certainly), Zooropa or Boy (probably) should go before War or NLOTH, but since a vote for one of those would be a waste at that point, I guess I'll have to choose between two pretty strong (but nonetheless uneven and flawed) records.
Interestingly, where both Boy and ATYCLB marked the beginning of something, and set the stage for what was to come (this is one of the reasons ATYCLB is more of an important record for them than War), War and NLOTH were the third act culminations of a U2 "era"...the first and their most recent. After War U2 went in a very different direction, as they did after JT and most certainly will after NLOTH.
War's best song, New Year's Day is one of my Top 5 U2 songs of all time. It was the first song I ever heard from them (actually, saw the video), and for that reason War is a sentimental favourite.
However, the best song on NLOTH, Moment of Surrender, is better than the best song on War, and is probably U2's best song since Streets.
So it's with great regret that I must cast my first vote in this series for War. Though I'd guess NLOTH will get voted off this round...which is kind of funny because has this contest taken place in the month's after it's release, I have no doubt it would have made it much further. I don't think that records aged well among the U2 faithful.