Electron/hole transfer mechanisms in DNA and polynucleotide structures continue to garner considerable interest as emerging charge-transport systems and molecular electronics. To shed mechanistic insight into these electronic properties, we carried out large-scale density functional theory (DFT) calculations (up to 650 atoms) to systematically analyze the structural and electron/hole transport properties of fully periodic single- and double-stranded DNA. We examined the performance of various exchange-correlation functionals (LDA, BLYP, B3LYP, and B3LYP-D) and found that single-stranded thymine (T) and cytosine (C) are predominantly hole conductors, whereas single-stranded adenine (A) and guanine (G) are better electron conductors. For double-stranded DNA structures, the periodic A-T and G-C electronic band structures undergo a significant renormalization, which causes hole transport to only occur on the A and G nucleobases. Our calculations (1) provide new benchmarks for periodic nucleobase structures using dispersion-corrected hybrid functionals with large basis sets and (2) highlight the importance of dispersion effects for obtaining accurate geometries and electron/hole mobilities in these extended systems.