As much as I loved the original, for me, the "remake" felt more like a sequel, or just another entry in the continuing franchise.
I really like both versions, as they are both good horror films in their own ways.
I always saw TCM03 as TEXAS CHAINSAW V, or a reboot, rather than a straight up remake. The feel, story elements and characters were different enough from the original, but similar enough to be a new part of the franchise. Sure, the basic plot is the same, but the plot has pretty much been the same in all TCM films.
Even though the events happen around the same time as they did in the original, the family is obviously different. In the first four films, Leatherface seemed to wind up in a different family, after PART 2, so this could possibly be another case of that.
I would like to see THE BEGINNING, but not as a prequel to a remake, but as sort of a "TCM 6," which happens to take place before the events in "Part 5", as I'm sure it will be.