Choose criterion of comparison two data samples

I have two data samples representing quality of two algorithms. I need to compare them and decide what algorithm is better. Quality depends of experiment number. i.e. it is progressing through experiments.
Please, help to decide what criteria should I use to determine what algorithm is better and what level of significance it provides. I thought of Mann — Whitney U-test and Student's t-test. Also, do I need to provide smoothing of dynamic series?

Data series can be provided if needed.