He's even got the gold watch on, very clearly, when he appears in the Flesh and Stone continuity in this episode. ... maybe it's the gold watch in the shot too, and we just underestimated the amount of shadow it was in? It seems really damn weird that they would give him a different watch for no reason all of a sudden, just for that one scene. Also, you have to assume that they filmed the whole scene, including the part that was only shown in Big Bang which clearly showed the gold watch, at the same time, back when they filmed Flesh and Stone. They wouldn't have rebuilt the set just for a few extra shots, it was planned out and filmed all at the same time. So there's even less reason to change the watch.

It must be the same watch? Just very shadowed so you can't tell it's gold?

EDIT - Yes, confirmed. Dammit. I used my fancy video player to tune up the contrast and brightness and such on the video, and you can see that it's the same watch as ever. It's not leather, you can see the lines of the gold watch on the band.

We were tricked by shadow.