The only dev board that I know of that has a FT2232H
with enough IOs connected to the FPGA so that it can be used in parallel mode (albeit only asynchronous, because AFAIR, the clock out is not routed) is the Numato Saturn:
https://numato.com/product/saturn-spartan-6-fpga-development-board-with-ddr-sdram/I've used it successfully in the asynchronous parallel mode.
The async FIFO mode of the FT2232H allows throughputs of up to about 8MBytes/s. Not nearly as much as you can get with the synchronous mode, but way higher than anything you could get with a USB to serial interface.
For the record, it's interesting to note that, while many FPGA dev boards include the FT2232H chip (because it can be used as a JTAG interface very easily), most of them only route the second channel as a UART interface, while routing a few more IOs would allow the async (or better yet, the sync) parallel mode. Of course, you can always quickly add this kind of interface using a FT2232H breakout board and connecting it to your FPGA board (keep connections short for parallel modes.)