Clustered Standard Errors vs. Multilevel Logit Model--Which one to use

I'm working on a project with 233 observations from school districts in 10 states. Observations vary from between 3 and 108 observations per state. I am not interested in the state effects. I am only interested in the district level effects (the district level is Level 1-- there is no data on particular schools, classrooms or students). I realize that I have to do something about intragroup correlations, but I'm not sure whether I should use clustered standard errors or a multilevel model. When I use a clustered model, everything seems to work despite high multicollinearity between two key variables. When I use a multilevel model, the two variables wash themselves out in terms of statistical significance.

Which method should I use and why? If there is some other method to use, please let me know.

Thanks in advance for your help.