The Asurans had numerous advanced technologies at their disposal. More or less, however, they chose to imitate Lantean technology (most notably city-ships, the Aurora-class, and ZPMs) on a massive scale because they desired to equal their creators; it was also the most advanced technology known to them. It is unknown if any of their technology is unique to them, but it is unlikely as the Milky Way Replicators were unable to perform any research of their own and the Asurans have never shown any desire to advance upon their creators. The Lantean technology that the Asurans do use is usually inferior to that of their creators by the time they left Pegasus as they only had access to the Ancient technology used when they were nearly wiped out. This means that the shields and weapons of their ships and possibly their personal firearms are not as advanced as the Lantean counterparts. For example, while Asuran drones are unable to directly penerate an Asgard shield, the newer design of drone weapons used by the Lanteans near the end of their war with the Wraith might be able to pass through Asgard shields, although it's unlikely. They would put the shield under heavy strain, however.
The Asuran sensor technology appears to be inferior to the Ancients, as they are unable to detect ships in hyperspace, leaving Asuras open for a sneak attack. (ATL: "First Strike", "Lifeline", "Be All My Sins Remember'd")
With the help of Elizabeth Weir, however, the Asurans did begin to research an alternative to ascension. (ATL: "Progeny", "Lifeline", "The Lost Tribe")
Although they are unable to create entirely new technology of their own design, they are capable of adapting their already existing technology to a variety of different purposes and create several unique devices.