I'm afraid that your professor has old-fashioned thinking. Modern FPGAs are enormously more powerful than DSP chips. However, FPGAs are generally more difficult to use than DSPs, so FPGAs aren't for everyone.
I use FPGAs for sonar signal processing. Each data set is up to 50 megabytes. I can't store that inside an FPGA, so I use SDRAM. The SDRAM is also useful for buffering the output data over ethernet.
Here's some Xilinx and _Altera FPGA info for DSP applications, including video processing:
http://www.xilinx.com/products/design_resources/dsp_central/grouping/index.htm
http://www.@ltera.com/technology/dsp/dsp-index.jsp