Regression and MANOVA are based on two different basic statistical concepts. MANOVA (Multivariate Analysis of Variance) is actually a more complicated form of ANOVA (Analysis of Variance). In both ANOVA and MANOVA the purpose of the statistic is to determine if two or more groups are statistically different from each other on a continuous quantitative scale.
Regression is based on the concept of correlation. Correlation will help you determine if two variables are significantly related to one another. If they are, then regression can be used as a predictive model to determine the future impact of one variable on another.
So how do you decide when to use which? Well if you want to make a dorky stats joke, go with ANOVA. For example, do you want to come ANOVA to my house later for a beer? If you are looking to determine a statistical value then the stat that you choose determines on your research question and the available data that you have.
For example if you want to know if the amount of time a student studies each week has an effect on their CSAP score then you would want to conduct a regression to determine if the two are related. If they are then you would be able to predict how much an incremental increase in studying would increase a CSAP score.
If you want to know whether boys or girls (two different groups) score higher in CSAPs, they an ANOVA would be the appropriate statistic.
