Many people think FPGAs have the advantage over GPUs in machine learning inference. See the Bing FPGA stuff. Mostly due to lower power operations, but also a higher level of customization e.g. optimized 1 bit math if you want it, leading to potentially higher speed or larger networks. The memory architecture of FPGAs can also offer advantages - e.g. bigger memories.

The GPU instruction set is limited for some applications because of SIMD. If the GPU threads aren't doing exactly the same thing then they stall. The FPGA can have parallel processes going on that are more differentiated. e.g. HMMs work better on FPGA than GPU.

Anything with low latency feedback (e.g. LSTMs) probably works better on FPGA.