I have the Lie Nielsen and use/like it quite a lot. The brass body is very nice. All of the machining is spot on. Fits nicely in the hand. Blade seems to last nicely, though kind of by definition I don't really push the edge of my apron plane to its limits.
I haven't used the Lee Valley, so I can't do a direct comparison. One thing in favor of the Lee Valley plane is that you can order it with a PMV-11 blade. I have other planes with PMV-11 blades, and IMHO they are superior. If you are think about using on plywood or woods that are heavy on silicon content (i.e. Ipe or Jatoba), the PMV-11 would be a clear advantage.