It's interesting--with 5.0, 5.0.1, and 5.0.2, NuPlayer was actually the default, but it was described as "experimental." You could uncheck it in Developer Settings to go back to AwesomePlayer. Now, with 5.1, AwesomePlayer is the default, and you can uncheck it to use NuPlayer. I think the "deprecated" term means that AwesomePlayer will eventually go away, to be replaced by NuPlayer. They may have changed the default back to AwesomePlayer due to some issues people were having with videos when 5.0 came out.
I actually haven't noticed any real difference between the two.