Background Right ventricular (RV) dysfunction is recognized as a major prognostic factor in left‐sided heart failure (HF). However, the relative contribution of RV dysfunction in HF with preserved (HFpEF) vs. reduced ejection fraction (HFrEF) is unclear. Methods and results Right ventricular longitudinal strain (RVLS), tricuspid annular plane systolic excursion (TAPSE) and pulmonary artery systolic pressure (PASP) were determined by echocardiography in 657 age‐ and gender‐matched groups of patients with HFpEF left ventricular ejection fraction (LVEF) ≥50%; n=219 and HFrEF (LVEF <50%; n=219) and in controls without HF (n=219) from an Asian population‐based cohort study. Across control to HFpEF and HFrEF groups, RV function deteriorated as measured by RVLS (−26.7 ± 5%, −22.7±6.6% and −18.2 ± 6.7%, respectively) and TAPSE (21.0 ± 3.9, 17.5 ± 5.1 and 14.7 ± 4.7 mm, respectively), whereas PASP increased (26.8 ± 7.1, 34.5 ± 11.9 and 39.3 ± 16.2 mmHg, respectively) (all P<0.001). Controlling for PASP in control, HFpEF and HFrEF subjects, the magnitude of RVLS/PASP (−1.06 ± 0.32, −0.75 ± 0.32 and −0.56 ± 0.36, respectively) and TAPSE/PASP ratios (0.83 ± 0.23, 0.54 ± 0.24 and 0.55 ± 0.29, respectively) similarly decreased across groups. Right ventricular dysfunction (by both TAPSE and RVLS) was independently associated with left ventricular systolic dysfunction and atrial fibrillation, but not with PASP. Among patients with HF, both TAPSE/PASP and RVLS/PASP ratios were related to the composite endpoint of all‐cause death and HF hospitalization, even after multivariable adjustment hazard ratio (HR) 0.33; 95% confidence interval (CI) 0.14–0.74 and HR 3.09; 95% CI 1.52–6.26, respectively, with no difference between HFrEF and HFpEF. Conclusions Right ventricular dysfunction is present in HFpEF and is even more pronounced in HFrEF for any given degree of pulmonary hypertension. It is independently predicted by left ventricular dysfunction but not by PASP. Right ventricular–arterial coupling is prognostically important in HF regardless of LVEF.