When a nanoparticle is irradiated by an intense laser pulse, it turns into a nanoplasma, a transition that is accompanied by many interesting nonequilibrium dynamics. So far, most experiments on nanoplasmas use ion measurements, reflecting the outside dynamics in the nanoparticle. Recently, the direct observation of the ultrafast structural dynamics on the inside of the nanoparticle also became possible with the advent of x-ray free electron lasers (XFELs). Here, we report on combined measurements of structural dynamics and speeds of ions ejected from nanoplasmas produced by intense near-infrared laser irradiations, with the control of the initial plasma conditions accomplished by widely varying the laser intensity (9 x 10(14) W/cm(2) to 3 x 10(16) W/cm(2)). The structural change of nanoplasmas is examined by time-resolved x-ray diffraction using an XFEL, while the kinetic energies of ejected ions are measured by an ion time-of-fight method under the same experimental conditions. We find that the timescale of crystalline disordering in nanoplasmas strongly depends on the laser intensity and scales with the inverse of the average speed of ions ejected from the nanoplasma. The observations support a recently suggested scenario for nanoplasma dynamics in the wide intensity range, in which crystalline disorder in nanoplasmas is caused by a rarefaction wave propagating at a speed comparable with the average ion speed from the surface toward the inner crystalline core. We demonstrate that the scenario is also applicable to nanoplasma dynamics in the hard x-ray regime. Our results connect the outside nanoplasma dynamics to the loss of structure inside the sample on the femtosecond timescale.