Unless you’ve already made your reputation (and there’s not many that have), you’re facing a multistep hiring process, in which your goal in each step is to get to the next step. Most places get too many resumes, and need to thin the herd quickly. They aren’t going to be fair about it, because being fair would cost them time and effort without obviously getting them better people. Bitch about that if you like, but live with it.
Your resume isn’t going to get you a job. You want it to be free of obvious reasons not to hire you, buzzword-compliant with the job description, and standing out from the crowd in some way or another. It needs to survive the nontechnical HR person and the hiring manager, both. Put OS experience on your resume unless you know it will hurt (there are people out there who are anti-OS, and in today’s economy you can’t afford to avoid the clueless). That way you probably get to the next step.
Now, the OP did get to the next step, the coding test, and blew it. Nothing’s going to help you if you blow a step. If you can’t pass the test, odds are you can’t code up to company standards. This may be incorrect, but nobody’s going to take the time to find out. There’s enough candidates that passed that there’s no need to waste time and effort on also-rans.
Eventually, if you get through all other steps, you get to the point where you tell stories about your exploits, and how you approached problems, and you can talk about your OS experience. You’ll also want stories about how you got along in close proximity with annoying people and how you coped with being told to do something you didn’t want to do, and those will more usually come from regular work rather than OS experience.
You might find a way to introduce some particularly good code you wrote, and if it’s OS you can legitimately do that. Never show code you don’t have a clear right to show, or break confidentiality with anybody previous. You don’t want to give the impression you might treat them badly.
Don’t expect anybody to go through an OS project, cold, figuring out what you did and getting an idea of its quality. That’s a good deal of work, and nobody’s going to do that unless you’re going to be hired anyway.
So, while the benefits are there, they are limited. Don’t count on them to get a job.
And never denigrate in any way the ability to fill out a time sheet and estimate completion times. Those are valuable skills as a developer in any sort of commercial application.