It really depends on whether you include the memory in that count, as memory uses masses of transistors without being very interesting as most of those transistors spend their time just sitting there in a stable state. It's the transistor count (more properly, the gate count; gates can be thought of as multiple transistors fused together, yet they're truly a single thing in terms of manufacturing and layout) in the computational parts of the processor that is really interesting.

SpiNNaker is built using old ARM968 cores on an ancient process (because that was cheap, for various reasons). The SpiNNaker2 hardware (under design; I can't remember if it is next year or the one after when it is finalized) will be on a modern process that will let us pack ten times as many cores on per chip, with those cores being quite a lot more powerful. Which isn't bad; we're not a commercial outfit here…