I run a NH dealership and once owned an LS J2025H tractor (prior to my New Holland involvement) and must admit that I was impressed with what that little LS could do. So, yes, the Workmaster and Boomer (2013+) line are built by LS and there's virtually no difference between the two brands from a technical point, except for FEL's used on the mid and larger NH units are not from LS and have higher reach.
Parts availability through New Holland will be better than from LS itself, from what I've seen and heard. NH stocks its own inventory of LS parts at its depots throughout the US and most parts can be had next day if needed, or 2-5 days on regular stock order.
Why buy NH over LS? Couple of reasons...stronger dealer support network from New Holland which translates into better parts and service availability, warranty coverage. You won't find a NH dealer who can warranty an LS tractor, even though it's the same thing. Better financing from CNH vs. LS. Talking zero to 2% rates vs. 6-10% rates from LS's third party lenders. When you factor that in, you're about the same money or a little less for the NH when interest expense is totalled up. Lastly, I think the NH versions just look better with their deeper blue hue and iconic cat eye grille/light front end and will undoubtedly have a bit higher resale value than their LS counterparts for reasons stated above. I was a huge fan of the older Shibaura-built New Holland tractors but will admit the LS units have sold well and been pretty reliable. Just my two cents.