If this is a repeat post, please forgive me but I do not see a message I posted last Friday.
In addition to checking scree plots, and performing parallel analyses to determine number of factors to extract, I also check various fit indices. When using WLSMV, I use the RMSEA, CFI, TLI, chi-square and SRMR fit stats.
There are times when I might try a ULS estimator. To my knowledge, no other package except CEFA produces RMSEA or chi-square when using ULS. I note that ULSMV produces all the fit stats produced when using WLSMV.
I have checked the technical appendices. Except for a description of how ULSMV computes df, I can find no other reference to how ULSMV works. Aside from the calculation of df, are there any differences between ULSMV and ULS that I should take note of, or should the two provide identical results.