Menards has a decent 1/4" birch ply, and I like using that because it is cheaper then going to Rockler or ordering online. I tend to buy enough for a project or two at a time, not a whole sheet.
If I am framing a project I lean towards 1/8" because using 1/4" can make you run out of room in the rabbet. It is also lighter and sometimes I care about that. I also like that when stack cutting there is twice as many pieces in the stack, so when stack cutting I like to use 1/8".
I think it is a lot of personal preference and what you have available.
MrsN