Rather than answering this with a subjective answer, I went to Bing.com and looked up how loud roosters, chickens and dogs are as measured in decibels. It took a lot of references to find this, so I'm not listing them all, but here is what I found:
The average chicken - 60dbs
The average rooster crowing 100dbs
The loudest rooster recorded 113dbs+
A very large dog barking 100dbs
So, the original question mentioned 200 to 300 feet between neighbors. In my county, Escambia County, Florida, the chicken reg says one may not have a roo unless they are at least 150' from the nearest neighbor. According to our county regs, you would be in compliance, but you would need to check the regs in your own county to be sure.
The comments about a fence are pertinent, too. I have a six foot privacy fence between my property and my neighbor (who also has chickens.) Neither of us complains about the other's roos because they all crow all day. We just try to get along, even though we both know there is not 150' of separation between us. The neighbors on another side are family and they won't say anything to anyone, and the other neighbors are always indoors and don't hear the chickens, anyway.
We all also live within one mile of a NASCAR track, none of us are bothered by the noise emanating from there, and we are three-quarters of a mile from a high school football/baseball field. Since the racetrack brings about a million dollars/year into the community, and the school is an "attractive nuisance," nothing will ever be done about either of them.
So it's all relative.