One part of mindfulness meditation is deliberate practice at directed focus, and that practice improves your ability to think about what you want to think about rather than what your mind wanders to. There's another common practice where you actually intentionally practice allowing your mind to wander, and consciously choose to dismiss those thoughts.
I see mindfulness meditation as orthogonal to actual prayer, a little axe-sharpening that improves not only my prayer life but my general thought processes as well. If I only have time for one and not the other, obviously prayer is more important.
[0] For people who don't know, the Rosary is a series of meditations on different aspects of the lives of Jesus and Mary and the ministry of Jesus, in the form of an easily-memorized sequence of rote prayers. The rote nature of the prayers allows the person saying the rosary to use the brain's fuzzy focus to think about each aspect in turn. In total it consists of the Apostle's Creed, 6 "Our Father"s, 53 "Hail Mary"s, 6 "Glory Be"s, and one "Hail Holy Queen", taking between 10 minutes (if you're in a rush) and 20 minutes (if you're sleepy).
There's a huge difference that you have to experience with practice in order to begin to appreciate. Learning how to get out of your typical all-consuming "thought loops" is a skill worth having and cultivating.
I'll stick with the Rosary thanks.