Wire arc additive manufacturing (WAAM) technology is being employed in industries such as aerospace, maritime and automotive to produce high-valued metallic parts. With a growing demand for products with complex structures, it is crucial to develop an effective and reliable method for fabricating such parts to meet the demand. Currently, cold metal transfer (CMT), is one of the waveform-controlled short circuit transfer processes, commonly adopted in the WAAM process to fabricate medium to large-scale parts due to its perceived low heat input. However, the approach of using synergic control of wire feed speed and torch travel speed to control weld bead geometry in CMT may not be applicable for fabricating parts with complex structures. In these circumstances, surface tension transfer (STT), a waveform controlled short circuit transfer process, or one of the alternative variants of controlled short circuit transfer with low heat input, may provide more options to control weld bead geometry. There appear to have been few systematic investigations of alternative controlled short circuiting variants for use in WAAM. This paper provides a comparative study to explore the potential of the STT process for fabricating parts with complex geometries in WAAM. Firstly, the working principles of the STT and CMT processes are reviewed. Then, the impacts of welding parameters in the STT and CMT on weld bead geometry are analysed based on experiment results. Finally, a comparison between these two welding processes with regard to flexibility in welding parameter adjustment, heat input and overlapping performance is conducted. Finally, a comparison between these two welding processes is conducted from three critical aspects: (i) Flexibility in parameter adjustment: STT has 333 % and 174 % larger average width and height variation ranges than CMT; (ii) Heat input: STT's heat input is 74.66 % higher than CMT's at TS = 300 mm/min; (iii) Overlapping performance: the average surface roughness of the tested CMT and STT groups is 0.1312 and 0.1823, respectively. Suggestions for using STT and CMT to fabricate parts with complex geometries are provided accordingly.