It was stated in an episode commentary that the Ori pulse cannons are ion-based, just as the Tollan's ion cannons are. Since the Ori weapon is unable to penetrate Asgard shields, it seems unlikely that they would fall to a Tollan weapon that operated on the same principles. So, in Tollan Ion Cannons VS Asgard ships and shields, the Asgard would almost certainly emerge as the victors.
While we never see Tollan and Asgard technology pitted against each other, it is probably safe to assume that the Asgard are more technologically advanced than the Tollan. They are clearly much much older than the Tollan, who are descended from an Earth culture even though they've surpassed us technologically, and judging by the development of new weapons to use against the replicators and the Ori, they have clearly continued to progress all this time.