Short answer, no effective difference.
A restart (at least in a Unix environment, which the Mac is), dumps EVERYTHING, and boots fully from a zeroed state. ALL processes are released and reinitiated from scratch. Even if there were anything residual in any cache, it would be overwritten anyway when the system was being restored.
I think the theory being put forward is that since some of the caps haven't fully bled off, there may be residual data in some of the registers. Unless they can state absolutely the decay rate of those, then "ten seconds", or any other SWAG'd delay, is basically bollocks.
This is more ancient technology concept, and since most Windows users have NEVER seen what actually goes on, process-wise, in detail, it's become more computer urban legend/dogma than anything else.
You could posit that a restart is easier on the microelectronics as they don't have time to suffer from thermal expansion because of short-cycle cooling & reheating. That, as well, is debatable, but certainly a stronger theoretical argument than any nebulous "data left in cache" claim.