In this experimental study, we explore the potential implementation of logic operations using the interference of propagating spin waves within a device composed of intersecting yttrium iron garnet waveguides with submicrometer width. Our investigation reveals the significant influence of finite-size effects on the performance of the microscopic devices. In particular, we observe that their efficiency depends on the wavelengths of the involved spin waves in relation to the size of the interference region and is reduced by multimode spin-wave propagation. These findings highlight crucial factors to be considered when designing magnonic nanodevices operating with short-wavelength spin waves, providing valuable insights for optimizing their performance in practical applications.