Inside a vertical, circular cross section duct which is hotter inside than outside (this difference is called delta-T) there's a fast streaming core. The rest of the gases in the duct are built up in layers, the closer to the wall of the duct the lower velocity and the lower the temperature. Against the wall, the last microns are effectively at a standstill, causing all the drag that is evident in a round stove pipe, apart from temperature differences. It's easy to see why the 4" pipe is not as capable of transporting gases compared to an 8" pipe, the high velocity core is much smaller and the wall is closer by. So drag is a comparatively large factor. I count this as a minus point.
The volume of gases which are inside a J-tube does heat up and expand, cools down and contract, that's true. But by how much and how effective is that? Complete combustion is a misleading phenomenon, since only the moist is visible we tend to think it isn't much. Air is expanding not as much as one would think, from 68ºF to 1900ºF about 4.5 times. In the chimney there need to be some delta-T left for to keep the draft going, say 200ºF. At that temp, air has been shrunk to 1.2 times it's original volume, so inside the J-tube it's 3.3 times its volume as compared to in the chimney. So this seems to predict the chimney pipe shouldn't be smaller than the rocket's system size by a factor of 3. An 8" pipe is roughly 50"sq., and a 4" pipe is 12.6"sq. csa, this is a factor of 4 smaller, fat chances are a 4" pipe would strangle the 8" system. This would be the second minus point in my opinion. But a 6" pipe looks like it should work in this respect.
But... this is only about drag and air expansion, what about water? This is another story altogether, at 212ºF it will expand roughly 1500 times! In the fuel itself is only the left-over moist from the drying process, which could be anything from 25% to 10% of fuel weight. I am not as good in calculating in cubic feet so I leave that to somebody else. On top of the fuel moist there's another effect, the combustion process itself produces heat, carbon dioxide and... water! This is quite a bit more, some people say it's close to half the original weight of the dry fuel. If this need to expand 1500 times also there's no chance on earth one could vent an 8" system with a 4" stove pipe, even when it is free. I would count this as negative 3.
When I had to choose and being tight on money I would choose a 6" pipe to vent the 8" system but take every precaution to never restrict the system anywhere else. The slightest constriction would then muffle the rocket because there's no more slack left. By the way, a batch box is quite another animal, not really comparable with a j-tube although they make the same peculiar noise most of the time. The burn rate of a BBR is much higher so it is better to have a chimney that's bigger as opposed to smaller than system size.
Nearly forgot: even when it would work to vent an 8" system with a 4" pipe starting it cold would be a nightmare. A rocket heater isn't a self-starting apparatus, there need to be a delta-T before there would be any draft in the system so the fire wouldn't smother itself.
For temperatures and expansion rates: see this
very comprehensive piece of text from Erica.