I want to know the difference in speed and how drastic it is. I'd like numbers but whatever else is fine too.
PCIe 2.0 offers a theoretical throughput of 5GT/s (gigatransfers per second, or billions of binary transfers per second)
PCIe 3.0 offers a throughput of 8GT/s.
The biggest improvement from 2 to 3 was in processing overhead, or how much power is needed to make the technology run correctly. With PCIe 2.0, the processing overhead was 20% (essentially, 20% of the "power" put into the system was not used for actual results). On PCIe 3.0, that overhead was reduced to about 1.54%
As for actual data bandwidth, the speed of 3.0 is roughly double that of 2.0. 3.0 offers 985MB/s per lane while 2.0 offers 500MB/s per lane