Using large-scale DFT calculations, we investigate the structural and electronic properties of both armchair and zigzag graphdiyne nanotubes as a function of size. To provide insight into these properties, we present new detailed calculations of the structural relaxation energy, effective electron/hole mass, and size-scaling of the bandgap as a function of size and chirality using accurate screened-exchange DFT calculations. These calculations provide a systematic evaluation of the structural and electronic properties of the largest graphdiyne nanotubes to date, up to 1296 atoms and 23328 basis functions. Our calculations show that zigzag graphdiyne nanotubes (GDNTs) are structurally more stable compared to armchair GDNTs of the same size. Furthermore, these large-scale calculations allow us to present simple analytical formulas to guide future experimental efforts for estimating the fundamental bandgaps of these unique nanotubes as a function of chirality and diameter. While the bandgaps for both the armchair and zigzag GDNTs can be tuned as a function of size, the conductivity in each of these two different chiralities is markedly different. Zigzag GDNTs have wider valence and conduction bands and are expected to have a higher electron- and hole-mobility than their armchair counterparts.