Strengths of mixed model

Hello forum,

I am doing a clinical trial with crossover design and repeated measurements. (4 treatment groups and 11 subjects.)

I have been advised by local statisticians to use the xtmixed command i STATA.

However, I am now unsure on how to describe the methods used, as I am not in to stat-language. I am considering to write something like:

....mixed model with treatment group as fixed variabel and subject ID as random variabel, followed by a Restricted Maximum Likelihood test for significance.
Do you have any comments?

At my research facility, we traditionally use a ONEWAY ANOVA approach with a t-test and Bonferroni correction for the same kind of research. Can you, please, explain briefly, why (or if) a mixed model is superior to an ANOVA approach in crossover designs?

Kind Regards