Seaborn uses matplotlib under the hood, rendering your question irrelevant. Seaborn is nice and provides a convenient way to use complicated matplotlib features. I use it quite often, but for very specific customization you'll need matplotlib functions on top of your seaborn plot.

Neither of them is designed for statistical testing, although it interacts with other statistical packages.

While matplotlib is used more frequently, this is mostly due to it being much older (after all, as WouterDeCoster said, searborn uses it). Having said that, I wouldn't start a new project with matplotlib only. Seaborn's plots both look nicer by default and in the end can be tweaked the same way as matplotlib.

You didn't mention plotly, which is too bad. As long as you're not trying to make large heatmaps or anything too overly complicated then it's relatively easy to use and looks nice. If it's useful in deciding, I was able to reimplement all graphical output from deepTools in plotly in about a week, so you can do standard stuff relatively easily.

please read seaborn introduction:

https://seaborn.pydata.org/introduction.html#introduction