Asthma and chronic obstructive pulmonary disease (COPD) have distinct and overlapping genetic and clinical features. We hypothesized that polygenic risk scores (PRSs) for asthma (PRSAsthma) and spirometry (FEV1 and FEV1/FVC; PRSspiro) would demonstrate differential associations with asthma, COPD, and asthma-COPD overlap (ACO). We developed and tested two asthma PRSs and applied the higher performing PRSAsthma and a previously-published PRSspiro to research (COPDGene and CAMP, with spirometry) and electronic-health record (EHR)-based (MGB Biobank and GERA) studies. We assessed the association of PRSs with COPD and asthma using modified random and binary effects meta-analyses, and ACO and asthma exacerbations in specific cohorts. Models were adjusted for confounders and genetic ancestry. In meta-analyses of 102,477 participants, the PRSAsthma (OR per SD 1.16 [95% CI: 1.14-1.19]) and PRSspiro (OR per SD 1.19 [95% CI: 1.17-1.22]) both predicted asthma, while the PRSspiro predicted COPD (OR per SD 1.25 [95% CI: 1.21-1.30]). However, results differed by cohort. The PRSspiro was not associated with COPD in GERA and MGB. In COPDGene, the PRSAsthma (OR per SD: Whites: 1.3; African Americans (AA): 1.2) and PRSspiro (OR per SD: Whites: 2.2; AA: 1.6) were both associated with ACO. In GERA, the PRSAsthma was associated with asthma exacerbations (OR 1.18) in whites; the PRSspiro was associated with asthma exacerbations in white, LatinX, and East Asian participants. Polygenic risk scores for asthma and spirometry are both associated with asthma-COPD overlap and asthma exacerbations. Genetic prediction performance differs in research versus EHR-based cohorts.