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The are several ways you can tell which star is the bigger and/or brighter of the two, but most are beyond the scope of your study. The main one is using spectroscopy to look at the spectral lines and their intensity. You can tell from this whether the star is a MS, giant or supergiant (therefore how bright it is), what spectral class it is and even how rapid the orbit of the two stars is. You can then use stellar theory to determine the size of each star.
You can also identify the EB type from the shape and timing of the light curve. beta-Lyrae variables have a rather gradual slip into the eclipse cycle on both the secondary and the primary eclipse as one (or both) of the star is extended and it's hard to pin down where the eclipse starts. Algol type EB's have a relatively easy to define eclipse start as both stars have distinct stellar limb boundaries....the timing is reasonably sharp.
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