Moderately preterm infants (32–36 weeks of gestational age) have an increased risk of worse health and developmental outcomes compared to infants born at term. Optimal nutrition may alter this risk. The aim of this study was to investigate the neurological, growth, and health outcomes up to six years of age in children born moderately preterm who receive either exclusive or fortified breast milk and/or formula in the neonatal unit. In this longitudinal cohort study, data were collected for 142 children. Data were collected up to six years of age via several questionnaires containing questions about demographics, growth, child health status, health care visits, and the Five to Fifteen Questionnaire. Data on the intake of breast milk, human milk fortification, formula, and growth during hospitalization were collected from the children’s medical records. No statistically significant differences in neurological outcomes, growth, or health at six years of age were found between the two groups (exclusive breast milk, n = 43 vs. fortified breast milk and/or formula, n = 99). There is a need for research in larger populations to further assess potential effects on health and developmental outcomes when comparing the use of exclusive versus fortified breast milk for moderately preterm infants during neonatal hospitalization.