After running 9 tires through our recent comparison tests, I have been quite surprised to see how much tires can improve cornering ability and climbing efficiency.
Climbing Efficiency: The best rolling tires made a bike feel several pounds lighter. Some tires literally would stop rolling without pedaling, while the best rolling tires seemed to continue rolling on their own as if they had an electric motor attached.
Cornering Ability: Finding tires with cornering grip was not a difficult task. Combining that cornering grip with good steering feel to be able to make the most of that grip was less common. The best front and rear tires that we found for cornering combined both good levels of cornering traction as well as constant communication of trail conditions and available grip. Different tires could make the same bike change from handling like a monster truck to feeling like a sports car.
Good tires aren't cheap, but if you've spent good money on your bike, cutting corners on poor tires is penny-wise, pound foolish. Tires can make more of a difference on how your bike handles than almost any other upgrade you can do to your bike.