What are the differences running subs at 4ohms vs 1omh?

Their are no real benefits for trying to find a 4 ohm amplifier over a 1 ohm amplifier. The sound quality differences are so small you would test equipment to tell them apart. The rest of the things you list are not true.

Get a 1 ohm stable amplifier and be happy.

has nothing to do with sound quality. Your subs are rated at a certain "ohm" value. depending on how they are wired the ohm value of the two subs can go up or down. an amp is rated by how low of ohm load it can handle and you need to mkae sure your speakers and amp are matched right. when you cut your ohms in half you double your watts. Every time you double your ohms you cut your watts in half. You need to go do some more reading because you are going to ruin your equipment if you do not have a full understanding of series/paralell circuits and the effect it has on resistances.

Running your subs at 4 ohms will make your amp work less hard but in result, there not as loud. thats pretty much it. wire it to 1 ohm if your wanting to get max power.