This study provides a comparison of the results of latent class analysis (LCA) and mixture Rasch model (MRM) analysis using data from the Trends in International Mathematics and Science Study -- 2011 (TIMSS-2011) with a focus on the 8th-grade mathematics section. The research study focuses on the comparison of LCA and MRM to determine if results obtained differ when the assumed psychometric model differs. Also, a log-linear analysis was conducted to understand the interactions between latent classes identified by LCA and MRM. Response data to the three booklets were used to run latent class analysis using Mplus 7.31 (Muthén & Muthén, 2012a) for LCA and WINMIRA (von Davier, 2001a). The findings of this paper do not reveal unequivocally whether a model based on primarily qualitative differences (LCA), that is, different strategies, instructional differences, curriculum etc. or a model including additional factors of quantitative differences within strategies (MRM) should be used with this particular dataset. Both of the tests provided similar results with more or less similar interpretations. Both techniques fit the data similarly, a result found in prior research. Nonetheless, for tests similar to TIMSS exams, item difficulty parameters can be useful for educational researchers giving potential priority to use of MRM.