Neopolitan style:

• Una Pizza Napoletana is probably the "best" Neapolitan style. But it's on the doughy end of the Neapolitan spectrum (still thin in the middle, but with big puffy edges) and it's a fine dining event that you need to reserve exactly three weeks in advance, not a place you usually just stumble into (although they occasionally take walk-ins).
• Lombardi's is more Little Italy than Lower East Side and it's been several years since I've had a pie there, but it was a very good thin-crust Neopolitan pie the last time I went--and claims to be America's first pizzeria, which adds a little extra panache.
• Saluggi's on Grand Street is somewhere between a Neapolitan and NY-style pie, also very thin crust. I'm not sure it's going to make any "best" lists, but it's pretty good, and it's a relatively big place (more of a sports bar than a restaurant) where it's never hard to get a table.

NY-style:

• Grand Street Pizza is a newcomer on the LES that is quite good. Thinner than most NY-style joints in a small but hip shop.
• Sauce Pizzeria now has a few locations, but the one on the LES serves a decent thinner-than-average NY-style slice or pie.
• Scarr's seems to be the most written up LES pizza joint (except maybe Una) and (like Una) made the Pete Wells NYTimes "best 100 restaurants" list. It's a very good example of a classic NY slice and served in a throwback hipster setting that attracts an interesting crowd (it's also on a cool block with a fun mix of galleries, bars/restaurants, and Chinatown borderland industrial stuff). But the couple times I've gone there I haven't been blown away. It's great, but not life-changing, and I would say Grand Street Pizza and Sauce are in a similar category quality-wise (and the others might have slightly thinner crust).

My advice: try several of them and report back!

(FWIW, my kids' favorite pizza place in the neighborhood is Don Alphonso's Pizza Shack at the far eastern end of Grand Street. They make everything from scratch with fresh ingredients and put out a very flavorful slice that's another good example of the classic NY-style pie. But it's definitely on the doughier end of the NY-style spectrum.)