I do yoga because I feel like it incorporates both mobility and stretching as well as some strengthening. I think both are probably good to do but stretching might be slightly advantageous. I think it’s also dependent on how old one is because mobility work would be beneficial the older we get because mobility goes down with age.
I also do hip and spine mobility work and try to work on some other joints too every day. That way I can mix it up every time.
Yes, I carry my stress in my shoulders nad upper back, and this has greatly affected my mobility in general. Working this out is a daily commitment.