I've read quite a few discussions pertaining to this topic.
In the counter argument, it's been highly noted that Borg will eventually adapt to any technology used against them. But as shown in two different cases that's not completely true. As with the case of Species 8472, they can't understand what they don't assimilate. In the final episode of Voyager, they had trouble adapting to technology that was 20ish years more advanced then the modern Federation until they assimilated Admiral Janeway and her shuttle.
So in regards to Asgard and Ancient technology, it's completely foreign to the Borg as it's not based on anything they know. Unless they assimilate a sample of it, a lot of their ships are going to get sunk. They are not like the Replicators as they seem more intuitive coming up with technology that even Asgard are able to understand.
But the key piece of technology that I always wonder to why it was never brought up in discussion is why not use the anti-replicator weapon? What binds the Borg as a collective are essentially the nanites in their bodies. Shut those down, the drones aboard the ship will either die or be free.
In the SG shows, the Replicators were only able to adapt because they had time to study the technology directly. The Asurans only adapted because it was based off technology they were familiar with.