My experience has been that ice baths are way better than cold showers. I find the cold showers a miserable, wretched experience suitable only for when I'm traveling.
By contrast. Ice baths are a meditative experience for me.
Muscle receovery is the least important reason to practice deliberate cold exposure. In fact, you'll get more out of your workout if you use exercise to recover from the ice, rather than the other way around.