One major advantage of additive manufacturing is the high freedom of design, which supports the fabrication of complex structures. However, geometrical features such as combined massive volumes and cellular structures in such parts can lead to an uneven heat distribution during processing, resulting in different material properties throughout the part. In this study, we demonstrate these effects, using a complex structure consisting of three conic shapes with narrow cylinders in between hindering heat flux. We manufacture the parts via powder bed fusion of Ti6Al4V by applying a laser beam (PBF-LB/M) as well as an electron beam (PBF-EB). We investigate the impact of the different thermal regimes on the part density, microstructure and mechanical properties aided by finite element simulations as well as by thermography and X-ray computed tomography measurements. Both simulations and thermography show an increase in inter-layer temperature with increasing part radius, subsequently leading to heat accumulation along the build direction. While the geometry and thermal history have a minor influence on the relative density of the parts, the microstructure is greatly affected by the thermal history in PBF-LB/M. The acicular martensitic structure in the narrow parts is decomposed into a mix of tempered lath-like martensite and an ultrafine α + β microstructure with increasing part radius. The EBM part exhibits a lamellar α + β microstructure for both the cylindric and conic structures. The different microstructures directly influence the hardness of the parts. For the PBF-LB part, the hardness ranges between 400 HV0.5 in the narrow sections and a maximum hardness of 450 HV0.5 in the broader sections, while the PBF-EB part exhibits hardness values between 280 and 380 HV0.5.