I have done absolutely no work to either one other than lapping and honing the blade on the Veritas. I have been using the Veritas some, but it has been treated with care.
Both planes are machined very nicely. Checking the sole longways against the blade of my Starrett combo square, I can see no light at all with the LN. With the Veritas only a bit of light is visible between the straight edge and the adjustable mouth piece. The rest of the sole appears to be perfectly flat. Checking both planes crossways with the combo square the Veritas shows just a sliver of light in the center checking in various places while the LN shows none until you get to the rear 1/4 where a faint light becomes visible. I can see no value in further flattening the sole of either plane and I've become rather anal about this sort of thing lately.
The LN takes a slight lead in fit and finish. The casting is smoother inside and the handles have been rounded with a little more care. The bronze frog and lever cap on the LN look nice on it but I find the overall look of the Veritas quite attractive as well.
Both planes came with A2 steel blade machined nicely but not honed. The Veritas was easy to lap as it was quite flat out of the box so I just had to remove the grinding marks to get a mirror finish. The LN blade appears at first glance to have been ground with a finer grit but I think I can see some deeper scratches in there. I'll know better once I lap and hone it.
I find the Veritas rear handle much more comfortable since it's a little taller and I can get my fingers wrapped around it. I don't have gorilla hands so I can imagine this being even more of an advantage to some. Right now, I feel the Veritas is a better value and will probably lean that way when choosing where to buy my next plane. Assuming both companies I'll have to use both side by side to be sure. I feel genuine pride in owning both planes.
I'm going out to make some shavings now!