As for New Hollands being rebadged LS machines, I cannot comment. I've looked at LS and a lot of things seem different between the two brands but I was probably comparing machines of different ages and designs.
What model years are you comparing?
There are several models that are rebadged LS machines for the past few years.
The older models prior to 3-4 years ago were not LS.
I didn't spend much time looking at new machines because they were way out of my price range. The machines I did look at were the Boomer 3040 and the 3045. They seemed to be newer versions of the TC models. I did a little research into the rebadged LS and found exactly what you stated. Only a few of the New Holland models are LS machines. I hadn't looked at any of those models in particular. Here is a link to a thread about this topic which you may have seen already.