To be short, the Arkentsone is more valuable.
Mithril was much more common and was traded among the peoples of Middle Earth while there only ever was one Arkenstone.
We even have an estimate of the original worth of mithril, the worth while it was still mined, thanks to The Fellowship of the Ring… Gandalf tells us that originally mithril had a value only ten times that of gold.
But mithrils value increased far beyond ten times that of gold because it is no longer mined thanks to Moria being overrun.
“What?” cried Gimli, startled out of his silence. “A corslet of Moria-silver? That was a kingly gift!”
“Yes,” said Gandalf. “I never told him, but its worth was greater than the value of the whole Shire and everything in it.”
Even with that increase in value, mithril still cannot compete with the Arkenstone. The Arkenstone’s value is measured in the trillions. Trillions, let alones tens of trillions, would easily purchase a large number of rural, agricultural, villages and all that they might possess.
The Arkenstone was also unique, being the only one ever found. The Arkenstone also has a massive sentimental value to Thorin and his family.
It’s uniqueness, its value in treasure, and its sentimentality leaves the Arkenstone as undoubtedly the most valuable.