Repeated measures ANOVA vs. Mixed Models

I'm trying to analyze the results of my Master Thesis with SPSS.
I've 3 experimental conditions (factor: Group) and for variable A every subject in each condition has 2 expressions (factor: Hemisphere).
I want to test the effects of these 2 factors on my dependent variable A. What I would like to test is:
- effects of Group on A
- effects of Group x Hemisphere on A
- effects of Hemisphere on A between my 3 Groups
- effects of Hemisphere on A whithin my 3 Groups

I wanted to use a repeated measures ANOVA. But then I came across mixed models. What is the difference between these two tests? Which one is more suitable for the kind of analysis that I want to perform?

Thank you very much for your help!