Hi,
you can see an FPGA like "programmed" hardware.
The delay from input to output can be in the small nanoseconds. With a controller or DSP it is in microseconds..
The FPGA can work a lot of calculations in parallel with variable bus width. A controller or DSP has fixed bus width and has to do the calculations in serial.
In a large FPGA an can implement a complete controller/DSP or only the parts of the controller/DSP you need. Additionally you can implement all the glue logic that is usually needed by a controller.
FPGAs are very flexible and complex. They have multiple clock generation mudules inside, they have RAM inside, they have high speed serial communication ports, they can communicate with multiple voltage levels at the same time.
A controller/DSP is easy to use. You have a fixed command set and fixed pin functions. All this usually is described in one document.
Both devices have their benefits...
...
Klaus