A key component of model predictive control (MPC) is the solving of quadratic programming (QP) problems. Interior point method (IPM) and active set method (ASM) are the most commonly employed approaches for solving general QP problems. This paper compares several performance aspects of the two methods when they are implemented on a FPGA for MPC applications. We compare the computational complexity, storage, convergence speed, and some practical implementation issues. We find that, in general, ASM gives lower complexity and converges faster when the numbers of decision variables and constraints are small. Otherwise, IPM should be a better choice due to its scalability. We also note occasional instability of both IPM and ASM when they are implemented in our FPGA, which uses single precision floating point arithmetic. The instability is mainly due to numerical error, which is found to be more serious in ASM than IPM in our current implementations.