The Brompton is generally upright. The Birdy will also be upright if you get it with the comfort stem (10 deg and adjustable height)
The Brompton will fold smaller but the Birdy should fold small enough for your needs.
The Birdy will be faster, more comfortable on rough roads, have better brakes, be more fun and be better for long rides.
I know the Birdy much better than the Brompton but most people seem to agree with the above.
David