Does it matter? Both countries are trying to change the demographic to their favor. India was not traditionally a united nation. China was, but Tibet was not traditional Chinese or even within the Chinese culture influence (unlike Korea and Japan). Neither really has a good historical claim to it. Maybe an independent Tibet would have a claim, but its border has been fluxing in history as well. Neither country has a tradition of allowing self determination. (It's like US and Canada fighting for an Indian reserve).
Also, it's not really about the land since it's pretty worthless, but the strategic location. Additionally, the domestic pressure is probably more important than any external considerations.
To be honest, I don't think either side cares that much. They have been fighting along the border for years, mostly for show.