Originally from Ontario, Canada, I live on Roatan full-time since 2007.
I have not stayed at either location but do know both of them. They are in the same area the difference being that Half Moon Resort is pretty much right on the beach, while Posada Arco Iris is across the sand road behind the Argentinian Grill.
The distance between the two is really minimal. Noise concerns at either (minimal at that end of West End.) Walking vs taxi for either will be the same. The only difference is if you want to stay at a location where you can step out your door and pretty much into the water. Then you will want Half Moon Resort.
Regardless of which you choose you will have a great time on Roatan. West End is a great base to explore the rest of the Island from. Be sure to arrange a visit to the East End of the Island. East End Tour with Friends - pictures
As well as a beach day on West Bay Beach, one of the top 10 beaches in the world. You can take a water taxi from West End to West Bay.
Welcome to Roatan, Enjoy!