My Saint puppy Elvis is a vivid dreamer. He snores and whines and barks in his sleep. He also tries to chase things and I think he even tries to eat while he is asleep. I find it super cute when he dreams unless he starts to cry.
One time I was watching TV and he was sleeping in the living room and I heard him cry, like really sad cry. I usually just ignore him when he is making noises in his sleep but this time I was concerned that he was having a bad dream. I got up and checked on him. He opened his eyes and lazily wagged his tail and went back to sleep.
I think that some dogs just have more vivid dreams than others just like in humans. Most of their biological functions are the same as humans so it would make sense that they go into such a deep sleep that they start to dream. I'm not sure if they dream more because they are anxious I just think some dogs dream more than others.