I did a simple CFA, y BY x1-x8, and outputted the scores. Those factor scores have a standard deviation of ca 0.5 (or a bit higher). SPSS gives me factor scores with an s.d. of 1 or almost 1; it only differs slightly between principal components, axis factoring, and using maximum likelihood. I tried to save scores as regression, bartlett, Anderson-Rubin, but all give similar results.
So now I'm not sure how to interpret the Mplus results. What kind of (CFA) factor analysis is performed by default, exactly? And with what method are the scores saved?
With maximum likelihood and continuous outcomes, Mplus uses the regression method to compute factor scores. It is known in the factor score literature that the standard deviation of the factor scores is not the same as the standard deviation of the factor. It may be that SPSS does a standardization after factor score estimation.