In terms of temps, yes, it should beat it. You probably won't see much improvement in overall performance, but their lower TDP (even the Q8400 has a slightly lower TDP than the Q6600) should help them run cooler.
Not quite the same chip, but in this review of the Q8200S (http://www.legitreviews.com/intel-core-2-quad-q8200s-processor-review_896), they compare the chip to its 95W TDP Q8200 sibling, & basically that the "S" series were geared towards OEMs building small form factor PCs (i.e. PCs that, with a combination of lower power draw & a higher max operating temp, would handle the lower air flow & higher change of elevated temps for that size of system). Good news, too, was that they were able to OC their Q8200S (per page 13 of their review, with their motherboard they managed to get to just over 3GHz with a 430MHz FSB/x7 multiplier on stock voltage, & DDR3 RAM was bumped up to 1600MHz; with voltage increases, they were able to bump that up to 3.15GHz & a 450MHz FSB/x7 multiplier, which let them bump the DDR3 up to 1800MHz. They mentioned being able to hit 475MHz on the FSB, but that was pretty much a wall even with watercooling & higher voltages).
I would say, if you can get the Q8400S, get it, because it'll run cooler & has a higher thermal margin than the Q8400. Plus, depending on your motherboard you'd have the option of OCing it.
EDIT: This page (https://hothardware.com/reviews/intel-core-2-quad-q8400s1?page=2) talks about OCing the Q8400, which is apparently very similar to the Q8200 (same FSB, just a x8 multiplier for the faster CPU frequency), & they were also able to get to 400MHz FSB before having to increase voltage (bumping it to 3.2GHz), & hitting a similar wall at 490MHz (3.92GHz for the CPU), although that wall apparently didn't involve out-of-range voltages or "more powerful" cooling (possibly meant they were only using air cooling?).