It's definitely the original, IIRC Gary owned that and the MM art at one point, and sold the MM art I think;
I believe the anecdote was that Sutherland destroyed the original artwork used for the first edition Monster Manual cover shortly before the book went to print. Sutherland was quite angry and embarassed by the quality of the illustration. I don't know if the anecdote was true or not, but I recall that was one of the stories that was circulated a few years back at the time of Sutherland's death.
I knew the DMG cover artwork had been purchased by a collector but I was not aware of where the PHB original cover art was. I'm happy to learn that Gary kept it the whole time. It is, without doubt, the most famous cover artwork in the history of RPGs.
There is no doubt in my mind that the PHB cover art is among the most valuable pieces from Gary's collection. I wonder if now is the right time to sell it, however.
Most of the items to be sold at the auction have value because they were strongly associated with Gary. Some old dice or an old game are merely some old dice or an old game. It is their association with Gary Gygax which makes them valuable.
Not so with the Trampier PHB front cover. That has value which stands apart from a strong association with EGG. Moreover, as it is artwork with a deep nostalgic resonance and is, literally, the most famous cover art work in the history of RPGs, I would expect that the piece would fetch even more at an auction 10 or 20 years from now.
Perhaps Gail Gygax might prefer to hold on to that piece for another day.