First: define your terms. Give us pictures!
Also, when do you have these interactions where messiness and neatness conflict? For me, the issue is courtesy. Everyone should be courteous. Both the neat and the messy people.
Messiness can be a style. But it can also be a sign of pathology. Normally, I would let things pile up on my desk for a few months, and then organize it all. But when I was manic, and then depressed, I stopped doing any organizing for more than a year. I simply couldn’t do it.
My wife is neat, and I have come to like things neat, especially with kids. We will never find anything if people don’t put stuff back where we think it should be stored.
I guess, to answer your question, messiness is more likely to lose things. My daughter just found 17 dollars she lost over a year ago. It had fallen into the couch. The clicker falls down there a lot. So when the next person comes in the room, and they can’t use the TV until they’ve found the clicker—that’s rude. Similarly, in the kitchen, if there’s no place to sit or eat because papers and packages are all over the place, that’s pretty rude, too.
It tends not to go the other way. Neatness and cleanliness gets praise. It is the sign of a well-organized person, with a life they can keep together. Messiness suggests mental illness and disorganization, and inability to cope. At least in my case, messiness was all three of those things. Anyone who knew the signs could have looked at my office and diagnosed me.
As to your own clutter: well, you should be the person to clean it up, when it must be cleaned. If you live with other people, the courteous thing to do is to keep your clutter to your space, but keep things neat in public space.
If you are messy due to creativity, you will know exactly where everything is. If you are messy due to illness, you won’t have a clue what’s in the mess. If it is a parent you have this fight with, you’re out of luck. If it is a roommate, you probably should strongly consider compromising, or keeping your mess to your room. If it is a spouse, I fear for the relationship. A couple can not be bothered by their partner every time they come home. It won’t last.