I'm certain someone more informed than I will soon answer you.
I 'think' the birch and poplar both have a tendency to break because of one grain direction. The plywood is a 'stack' of glued together, thin layers of wood with the grain running in different directions.
Because I buy only the thinnest plywood - 1/64'. 1/32' & a bit of 1/16' - I buy from
http://www.micromark.com
I think you'll find less expensive aircraft plywood at Loew's or places like that.