I think you might have misread kbob’s comment. I think he was talking about upgrading from one SSD to another newer SSD — not from HDD to SSD.
Say you have an SSD that consists of 8x16GB chips. Internally it's implemented in something like a RAID0 array, which is why they're so fast. If the capacity doubles / size shrinks by a factor of 2 and someone decides to stick 16x16GB chips in the next gen SSD then you will see a speed increase. On the other hand if they go for 8x32GB you won't.