Hard question to answer, in part because there are so many things called poplar. The only thing I've worked with is often called yellow poplar, but the sci, name is "liriodendron tulipifera," or tulip tree. A fairly soft wood, easy to cut and good for picture frames, architectural molding, and light furniture. The yellow poplar I used seemed to be fairly stiff, and able to take stress at 1" thick. Below that, it was somewhat bendy.
I've only once cut into cottonwood, one of the species also called poplar, and it was too soft and mushy for anything I could think of.
Check the piece you are thinking of working. If the grain is regular, and the length doesn't flex much, it will probably be OK if the stick is for style. I doubt it would be good for rougher use.