I'm the head of our Embroidery Department D).
So i'm a little biased (just a little )
Screen printing maybe seem like a good choice because it is a lot cheaper than embroidery, but will look like crap in not too long of a time.
Embroidery looks much better, costs more, but good embroidery will last many times as long as screen printing.
It all depends on what you are looking for.
It's a tough decision to make, but be sure you choose wisely.