Yes, they were firing at their max rate, but my impression was Patriots with their longer range were more effective.
Most likely the Patriot, which has longer range, has two shots per inbound; see, if there is a single bomb incoming, the RBS-23 has one attempt at it, and if SAM misses, adios. Patriot will shoot at max range, and if SAM misses, it will shoot once again at closer range. However, this is offset by Patriot also engaging aircraft at max range. At max range, Patriot has no chance against Gripen, so it just wastes reloads and illumination channels.