I have a set of paired measurements which were collected before and after some trigger for a set of users. Users can react differently to trigger, i.e for some measurements before trigger are larger than measurements after the trigger, for others it's the opposite, for the some measurements after trigger could be still smaller than measurements before the trigger of other person. I want to show that on average the measurements after trigger will increase. Total amount of measurements is 140. The distribution from which data was sampled is most likely not normal.
On one hand, to prove that I can simply split measurements into two groups 'Before Trigger' and 'After Trigger', and do a t-test to compare means of two groups.
On the other hand, I can take differences for each user separately and perform wilcoxon signed rank (or some other paired test) test on those differences.
Which of the methods is more preferable and why?
Edit added QQ plots, first one for measurements, second one for difference