By Psychometric properties, I do not mean Validity or Reliability. In RMT, they include DIF, Measurement Precision, Dimensionality etc. Analogous to these properties in CTT ??
there are some articles that compared CTT and IRT, e.g.,
Hambleton, R.K & Jones, R.W. (1993). Comparison of Classical Test Theory and Item Response Theory and Their Applications to Test Development. Educational Measurement: Issues and Practices, 12(3), 38-47.
MacDonald, P., & Paunonen, S. V. (2002). A Monte Carlo comparison of item and person parameters based on item response theory versus classical test theory. Educational and Psychological Measurement, 62, 921–943.
Kamata, A. & Bauer, D. J. (2008). A note on the relationship between factor analytic and item response theory models. Structural Equation Modeling. 15, 136-153.
Are you wanting a comparison of IRT (item response theory, which would include the Rasch model) and CTT? If so, most psychometric books now describe this (and then usually discuss IRT much more since this is now more used). They discuss how IRT measures are often about the items, while CTT are about the test. Therefore there is not a one-to-one correspondence between measures (though sources often have tables to help compare these).
there are some articles that compared CTT and IRT, e.g.,
Hambleton, R.K & Jones, R.W. (1993). Comparison of Classical Test Theory and Item Response Theory and Their Applications to Test Development. Educational Measurement: Issues and Practices, 12(3), 38-47.
MacDonald, P., & Paunonen, S. V. (2002). A Monte Carlo comparison of item and person parameters based on item response theory versus classical test theory. Educational and Psychological Measurement, 62, 921–943.
Kamata, A. & Bauer, D. J. (2008). A note on the relationship between factor analytic and item response theory models. Structural Equation Modeling. 15, 136-153.