That's because the 16 bit and 32 bit run out of different memory.
Did you follow the instructions in the board manual?
OK, From memory, open an sdk shell. type
ns recovery_configuration_apex_20k200.sof
after it has downloaded... type
nr default_board_image_apex_20k200.flash
Then unplug and re-plug your board. (powercycle it).THen all should be well.
You should also be on a later version of Quartus AND Nios!
Nios 2.0 still had no problems with the Apex design, but Nios and Quartus are numbered differently. If you look in the readme.txt you will see what version of Quartus your Nios kit was tested with.
Kerri