We study modulation properties of two-element phased-array semiconductor lasers that can be described by coupled mode theory. We consider four different waveguide structures and modulate the array either in phase or out of phase within the phase-locked regions, guided by stability diagrams obtained from direct numerical simulations. Specifically, we find that out-of-phase modulation allows for bandwidth enhancement if the waveguide structure is properly chosen; for example, for a combination of index antiguiding and gain-guiding, the achievable modulation bandwidth in the case of out-of-phase modulation could be much higher than the one when they are modulated in phase. Proper array design of the coupling, controllable in terms of the laser separation and the frequency offset between the two lasers, is shown to be beneficial to slightly improve the bandwidth but not the resonance frequency, while the inclusion of the frequency offset leads to the appearance of double peak response curves. For comparison, we explore the case of modulating only one element of the phased array and find that double peak response curves are found. To improve the resonance frequency and the modulation bandwidth, we introduce simultaneous external injection into the phased array and modulate the phased array or its master light within the injection locking region. We observe a significant improvement of the modulation properties, and in some cases, by modulating the amplitude of the master light before injection, the resulting 3 dB bandwidths could be enhanced up to 160 GHz. Such a record bandwidth for phased-array modulation could pave the way for various applications, notably optical communications that require high-speed integrated photonic devices.