Some health disturbances like neurodegenerative diseases are associated to the presence of amyloids. GNNQQNY and NNQQNY peptides are considered as prototypical examples for studying the formation of amyloids. These exhibit quite different aggregation behaviors despite they solely differ in size by one residue. To get insight into the reasons for such difference, we have examined association energies of aggregates (parallel β-sheets, fibril-spines, and crystal structures) from GNNQQNY and NNQQY using density functional theory. As we found that GNNQQNY tends to form a zwitterion in the crystal structure, we have investigated the energetics of parallel β-sheets and fibril-spines in the canonical and zwitterionic states. We found that the formation of GNNQQNY aggregates is energetically more favored than the formation of the NNQQNY ones. We show that the latter is connected to the network of hydrogen bonds formed by each aggregate. Moreover, we found that the formation of some NNQQNY aggregates is anticooperative, whereas cooperative with GNNQQNY. These results have interesting implications for deciphering the factors determining peptide aggregation propensities.