We present electric noise measurements of nanoscale biepitaxial YBa 2 Cu 3 O 7−δ (YBCO) Josephson junctions fabricated by two different lithographic methods. The first (conventional) technique defines the junctions directly by ion milling etching through an amorphous carbon mask. The second (soft patterning) method makes use of the phase competition between the superconducting YBCO (Y123) and the insulating Y 2 BaCuO 5 (Y211) phase at the grain boundary interface on MgO (110) substrates. The voltage noise properties of the two methods are compared in this study. For all junctions (having a thickness of 100 nm and widths of 250-500 nm), we see a significant amount of individual charge traps. We have extracted an approximate value for the effective area of the charge traps from the noise data. From the noise measurements, we infer that the soft-patterned junctions with a grain-boundary (GB) interface manifesting a large c-axis tunneling component have a uniform barrier and a superconductor-insulator-superconductor (SIS) -like behavior. The noise properties of soft-patterned junctions having a GB interface dominated by transport parallel to the ab planes are in accordance with a resonant tunneling barrier model. The conventionally patterned junctions, instead, have suppressed superconducting transport channels with an area much less than the nominal junction area. These findings are important for the implementation of nanosized Josephson junctions in quantum circuits.