For applique, all-cotton fabric is easier to work with than poly or poly blends. The cotton creases easier and holds a crease longer, plus cotton frays less around the edges.
For piecing, poly is more slippery than cotton, making matching complex patterns harder.
If you are making a quilt you want to last a very long time, it's a good idea not to mix cottons with polyesters. This is because polyesters do not fade over time. Cottons do fade. You really want all the fabrics to either fade together or not fade at all; mixing them can create quite odd-looking results down the line.