First off, let's use the terms "neat freaks" and "messy people" as pure adjectives with no judgment of them as people. Now, inside the mind of a neat freak is a need for order and, sometimes, perfection. Depending on the degree of neatness this person has will greatly impact their level of productivity. The neat person needs to have their exterior environment a certain way. Some folks in this category stay content with how they leave things and go about their business. The more extreme the neatness, the more concerns grow about just how neat and perfect the environment is. They may start to question just how neat/perfect it is. While they may or may not act on these questions, their mental capacity is diminished. They may even be looking at their neighbor’s work cubicle and wondering why they are so messy and envisioning a neat and perfect cubicle for their office mate. If they follow through with these thoughts, they expend energy on doing so instead of whatever other task is before them. Being neat is always their first priority.
On the other hand, messy people are totally okay whether their environment is clean or messy. It's almost like it doesn't matter. There is a certain level of non-pathological denial to the messy person as they either don't see mess, or they see mess but shrug their shoulders, going about their business. The main reason messy people may have greater productivity is because they put no thought into being messy or not. Cleaning and straightening up is something they just do or don't do. No mental energy is diverted from the task at hand.
To simplify, both categories are ways of being. Being messy requires little physical and mental exertion. Being neat requires thought and physical follow-up. Therefore, messy people have an easier time being productive and creative than neat people, as their focus can be 100% dedicated to the task before them. Neat people will have more difficulties due to the mental and physical distractions.