if you want each individual log moving you will need at least 1 joint for each log. if you just want the whole stack to move as one and only have the 1 joint and plan on no other physics interactions then anim dynamics is cheaper. add more than a few nodes and rigid bodies becomes cheaper.
I wish there was a combination of rigid bodies and anim dynamics. with rigid bodies even if translation is set to be locked the joints will still try and separate (collision with the sharing bodies is off). on top of that there ALWAYS seems to be some level of jittering. with anim dynamics you dont have to deal with any of that. if you set it to rotate only it only rotates that joint. But what anim dynamics does not do well is collision with small objects. with only being able to set sphere or planar limit (with a plane you cant even scale) it makes it very difficult to get good results of things interacting on a characters body. I want the predictability of anim dynamics results with the precision of rigid bodies.