Obviously this is a complex question. The question might also include the cell processor.
And there is probably not a single answer which is correct for other related questions.
In my experience, any implementation done in abstract fashion, i.e. compiled high level language vs. machine level implementation, will inevitably have a performance cost, esp in a complex algorithm implementation. This is true of both FPGA's and processors of any type. An FPGA designed specifically to implement a complex algorithm will perform better than an FPGA whose processing elements are generic, allowing it a degree of programmability from input control registers, data i/o etc.
Another general example where an FPGA can be much higher performance is in cascaded processes where on process outputs become the inputs to another and they cannot be done concurrently. Cascading processes in an FPGA is simple, and can dramatically lower memory I/O requirements while processor memory will be used to effectively cascade two or more processes where there are data dependencies.
The same can be said of a GPU and CPU. Algorithms implemented in C executing on a CPU developed without regard to the inherent performance characteristics of the cache memory or main memory system will not perform as well as one implemented which does. Granted, not considering these performance characteristics simplifies implementation. But at a performance cost.
Having no direct experience with a GPU, but knowing its inherent memory system performance issues, it too will be subjected to performance issues.