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So the article says that Freeman Dyson calculated that only one graviton capture event would happen per billion years in a detector the size of the Earth. The new experiment however proposes to use 15 kg of super-cooled Beryllium.

My question is: what's the difference between the proposed Beryllium slab and Dyson's theoretical detector?

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I don't fully understand it, but I think the difference is in the source of the gravitons rather than the detector. Dyson's earth-sized detector was imagined to be detecting gravitons produced by mass moving around within the sun, but this detector would be detecting gravitons associated with gravitational waves produced by ridiculously powerful events like black hole mergers, where two massive objects circle each other at mind-boggling speeds before colliding. It sounds like these are expected to produce vastly more gravitons, making a detection much more likely.

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