I understand on the rug, but keep it in mind that wall-to-wall carpet with padding is much more absorbent than a throw rug. Throw rugs do almost nothing. So consider that as you move forward.About bass traps, I have not compared measurements with panel dampers, nor have I seen anyone else do them. I'd like to, it would be an interesting study. But my hunch is that a cylindrical damper would not be nearly as effective as a large panel damper. A panel absorber both has the surface area and the ability to move, taking energy from a fairly wide band at LF. That's exactly what you want for damping.
My hunch is that tube traps are much more frequency and position sensitive, and that would make them much less useful. They would tend to provide the most absorption at their resonant frequency, and very little at other frequencies above and below. So that tells me that probably a comparitive study would show much more effective damping from panels. But even without a comparitive study, I know panel dampers work at LF. So the question for me becomes, can a tube trap be made that is as effective. Without answering that question, I'd stick with what I know will work, and that's false wall style panel dampers.
The thing is, if you were in a basement or somewhere with rigid walls all the way around, I'd be looking at that more seriously. But framed drywall rooms provide a pretty fair amount of LF damping already. They are pretty lossy because the walls have some give. So I wouldn't expect huge modal problem and if you wanted to go to the next level, I'd probably install multisubs before I'd look at bass traps or panel dampers.