My buddy just bought a 3039. He loves it. I am a Kubota man all the way, but I would pick the 3039 out of that group. If one of the contenders were a Grand L, I would be partial to it due to my good experience with them. Having seen his 3039, I can say that it is sure a nice machine with lots of features and a solid looking build.
Since you've had good experience with LS, I see no reason not to go that way. Surely more tractor than the Kub and JD you're looking at. I'm not as familiar with Branson. Their popularity and dealer support in my locale is non-existent.
Unfortunately, it seems as though the majority of Branson dealers are short term. I may be way off with that statement, but from all that I have read, there are only a few long time Branson dealers.
That LS is a deluxe machine vs the economy models of the JD & Kubota. While the Branson is a good machine, it is currently short some of the features that the LS has. Parts will be available for the Branson, but you would have to look and double check for a dealer and I'm not sure that the possible headaches would be worth having the additional weight capabilities.
Olympus, good luck with your final decision.
You have been posting and posting and posting threads on this selection, which is fine.
If the Branson is OUT, OK; move on.
Who knows the future in one year, much less ten years?
LS is the next heaviest of the four subject tractors.