I work a lot on GreenArrays, and I highly, highly doubt this claim. An F18 core has 1152 bits of SRAM on it, much less than these cores, which I believe I read have 32 KB. Moreover, while the Parallella is clocked (like almost every computer out there) the F18 is asynchronous.
From reading the parallella docs, it looks like that chips runs 5 W on a "typical workload" while the GA144 runs .25 W at an absolute theoretical maximum, for a 20x difference in energy consumption.
The parallella supports floating point though. I don't know how fast the GreenArrays run, but a factor of 20 doesn't seem impossible for a floating point intensive program. More on-chip memory can be beneficial too, if it helps to avoid accesses to off-chip memory. Of course, the unqualified claim from parallella is pretty useless…
That's why I'm asking. GA144 has 144 cores - but they are 18-bit wide, and the instruction set is rather unorthodox, even multiplication usually has to be programmed. Code density is pretty high, it's a Forth chip after all - but I suspect it is hard to achieve a good uniform load across the whole device... which might also be the case with Parallela. So we have to consider each claim differently. In general, though, they seem to be quite different chips.
You can program in floating point (I'm doing just that, with 6 cores performing Karatsuba-3 multiplication of 54-bit elements) but that is quite a bit slower than hardware DP multing (which Parallella boards lack too). FP multing will likewise be slower than hardware FP multing, which Parallella does have.
Sure, you can do floating point in software. My point is that dedicated hardware is very likely more power efficient at it. The same goes for memory: accesses to off-chip memory cost much more energy than accesses to on-chip memory. It would be very interesting to get energy and performance numbers for some real world application running on both chips.
From reading the parallella docs, it looks like that chips runs 5 W on a "typical workload" while the GA144 runs .25 W at an absolute theoretical maximum, for a 20x difference in energy consumption.
http://www.parallella.org/board/