As the EEG inverse problem does not have a unique solution, the sources reconstructed from EEG and their connectivity properties depend on forward and inverse modeling parameters such as the choice of an anatomical template and electrical model, prior assumptions on the sources, and further implementational details. In order to use source connectivity analysis as a reliable research tool, there is a need for stability across a wider range of standard estimation routines. Using resting state EEG recordings of N=65 participants acquired within two studies, we present the first comprehensive assessment of the consistency of EEG source localization and functional/effective connectivity metrics across two anatomical templates (ICBM152 and Colin27), three electrical models (BEM, FEM and spherical harmonics expansions), three inverse methods (WMNE, eLORETA and LCMV), and three software implementations (Brainstorm, Fieldtrip and our own toolbox). While localizations were found to be relatively stable, considerable variability of connectivity metrics was observed between LCMV beamformer solutions on one hand and eLORETA/WMNE distributed inverse solutions on the other hand, but also across implementations of the same source reconstruction procedure in different packages. To provide reliable findings in the face of the observed variability, we encourage verification of the obtained results using more than one source imaging procedure in future studies. Our results also show that while effective and functional connectivity are similarly consistent across different source reconstructions, effective connectivity is less reproducible than functional connectivity across participants. This finding may indicate that there are different phenotypes of directed brain communication patterns within resting state networks.