Three types of Josephson tunnel junctions, standard Nb/Al,AlO(x)/Nb, symmetric Nb/Al,AlO(x)/Al/Nb, and Nb/Al, AlO(x)/AlO(x)/Nb containing a double oxide layer have been investigated by means of temperature dependent I-V measurements, conductance-voltage measurements, noise analysis, and Auger Electron Spectroscopy scanning across the edge of a sputtered crater profile. In standard junctions frequently small leakage currents have been observed as well as resistance fluctuations, leading to telegraph noise. Both effects can be related to the direct contact between the AlO(x) and the Nb counter electrode. In none of the symmetric junctions leakage currents larger than 0.01 % of the theoretical maximum critical current have been observed. The sub-gap current of these junctions is dominated by single- and two-particle tunneling. The SNAP process, that was used to define the junction areas, affects the tunneling mechanisms below the sum-gap voltage, probably by the introduction of barrier inhomogeneities at the edges of the junctions. The AlO(x) barrier in symmetric and asymmetric junctions cannot completely be represented by a trapezoidal barrier shape. The metal-insulator interface between Al and AlO(x) in both junction types is probably not very sharp, which might be due to oxygen diffusion. The metal-insulator interface between AlO(x) and Nb in standard junctions can be represented by a step-wise increase of the potential barrier, indicating that this interface is very distinct. The AlO(x) barrier in double oxide layer junctions is not homogeneous and probably contains low barrier channels.