The One Ring provides great power, but its power is primarily to dominate others. Sauron already dominated, it is implied, nearly all of Middle-earth without the Ring. It is implied or stated at various points that with his limitless armies of vassals, he would be able to easily overwhelm the holdouts, again with no need for the Ring. Sauron originally made the Ring to specifically control the leaders of his enemies, but the Ringwraiths had already fallen to him, and the Elves would just remove their rings if he tried, as they had done previously.
By contrast, the Palantiri seem far more powerful. The Palantir that Sauron most likely had, the Ithil stone, could only look in a fixed direction, but it already would have permitted him to see most things along that line, with sufficient concentration. By contrast, had he obtained the Osgiliath stone or the other omnidirectional stone, he would have been able to see anywhere in Middle-earth, at an unlimited distance, eavesdrop on the communications of other Palantirs (in the case of the former), and possibly try to dominate the other users. The applications of such knowledge, especially in conjunction with the mental communication abilities of Sauron as a Maia, would be considerable, and it would be particularly bad for Sauron to have these capabilities if the Ring were not destroyed. Imagine Sauron being able to spy on Elrond's councils, or to send an assassin to kill one of his enemies who would know exactly how to slip past any protection. Indeed, his Eye (probably largely aided by the Palantir in his possession) was a significant threat even without the Osgiliath-stone.
Why, then, did both Sauron focus so much of his efforts on recovering the Ring, and his enemies so much on keeping it out of his hands, relative to the Palantiri, given the power of the latter?