Influenza viruses rapidly diversify within individual human infections. Several recent studies have deep-sequenced clinical influenza infections to identify viral variation within hosts, but it remains unclear how within-host mutations fare at the between-host scale. Here, we compare the genetic variation of H3N2 influenza within and between hosts to link viral evolutionary dynamics across scales. Synonymous sites evolve at similar rates at both scales, indicating that global evolution at these putatively neutral sites results from the accumulation of within-host variation. However, nonsynonymous mutations are depleted between hosts compared to within hosts, suggesting that selection purges many of the protein-altering changes that arise within hosts. The exception is at antigenic sites, where selection detectably favors nonsynonymous mutations at the global scale, but not within hosts. These results suggest that selection against deleterious mutations and selection for antigenic change are the main forces that act on within-host variants of influenza virus as they transmit and circulate between hosts.