The design of the transmit beampattern of a radar system aims to focus the energy of the transmitted signals to the desired spatial section(s) in order to enhance the direction of arrival (DOA) estimation at the receiver. In this paper, we consider this problem for both multiple-input-multiple-output (MIMO) and phased-array radar from the perspective of finite impulse response (FIR) filter design. For MIMO radar, we formulate the design as a feasibility problem (FP) and show its advantages over the existing methods. For phased-array radar, we use the spectral factorization technique which has been considered to be better than conventional filter design methods. It is shown that the two systems can achieve similar transmit beampatterns for identical number of transmit antennas and waveform energy. This is contradictory to the existing argument that MIMO radar can achieve more flexible transmit beampattern design over its phased-array counterpart. Simulation results are provided and discussed.