Comparison of groups with multiple measurements

I am designing a theoretical clinical trial in migraine and have some problems with the statistical analysis.

I will have 2 groups of 50 patients that get different treatments for acute migraine. They are followed during 2 months and record the time to effect for each migraine attack they suffer. This means that I will have a different number of measurements from each individual (e.g. patient 1 had 4 attacks, patient 2 had 8). My idea is to take the mean from each individual and then use that to calculate the mean of each group. To show that one group has a faster response than the other, should I use a t-test then or would it be a two way Anova?
Any thoughts would be appreciated.... Thanks!