This study assesses the use of Eulerian volumetric velocity images of the ventricular blood flow for estimating material properties of a physiological fully-dimensional FSI model of the systolic phase of the heart contraction. An efficient partitioned, semi-implicit FSI algorithm is employed, coupling a fluid fractional step scheme with a hyperelastic solid model. Cardiac mechanics model parameters characterizing the active contraction and epicardial wall boundary conditions, accounting for the external tissue support, namely the myocardial tissue contractility and the epicardial stiffness, are estimated from synthetic (i) solid measurements only, (ii) fluid measurements only and (iii) combined fluid and solid measurements. The parameters are estimated efficiently using a reduced-order unscented Kalman filter. Ground truth values of the estimated parameters are accurately recovered if the data provides a sufficient temporal resolution. While the contractility estimation only benefits by aggregating fluid measurements to the solid data by a reduced sensitivity to measurement noise, the epicardial stiffness is resolved more accurately when using fluid measurements instead of solid measurements.