What are the (dis)advantages of both sides of chart paper for drawing or painting?
The rough texture side is good at "grabbing" and creating friction. So it is better for things like pencils/graphite and for allowing it to deposit into the texture of the paper. The smooth side is better for precise application of liquid medium such as inks.

The texture side will be good at holding layers of powder medium such as soft pastels, and allowing for smudge-blending from areas where deposits have built up. It can also grip and hold things like oil pastels well because the texture gives them something to grip onto. 

It would be less effective to use oil pastel on the smooth side as there would be much more streaking; it would build up less and adhere less on the smooth side. Similarly, pencil/graphite would build up less and not adhere as well on the smooth side as there would be less friction from the paper's surface to allow the graphite to deposit.

For inks from things like markers, you could utilize the smooth side to help reduce "bleeding" from over-flooded areas since the smooth surface is more resistant.

An extreme example of how this works is if you imagine a sheet of glass vs a sheet of soft blotting paper. In the extreme, the smooth surface of the glass would repel ink, creating a surface tension at the edge of the liquid so that it forms small domes on the surface. The blotting paper would simple soak up the ink into a network of texture and absorbent fibers. In the less extreme (aka with the chart paper) this smooth surface on the paper is acting as a slight barrier and allows things like ink to glide along the surface without instantly being absorbed and spreading outwards.

When drawing, the ultimate way to find out how your tools and mediums will respond to the specific paper stock you are using is to experiment as there are many variables that could help overcome or take advantage of one side or the other for drawing (the thickness of the medium, the application, the tools, the tooth of the paper, etc).

Hope this helps!