Is there any type of hardware that has the same function as an FPGA but is cheaper? Probably a stupid question, because if it is cheaper, and does the same thing, why would anyone use an FPGA.
Not really, modern FPGAs are set up as multipurpose devices, complete systems on silicon, as it were but reconfigurable. They contain multiple memory blocks, memory controllers and DSP functions, all of these soak up most of the 'gates'. SHA256 needs only the gates, and even then logical function blocks in FPGA are very inefficient at implementing them.
Might be slightly better for SCRYPT mining, but never looked into it, but would probably still be beaten by an asic solution by an order of magnitude.