Apple customer service has been quite useful, however it has taken me lots of time and effort while I was effectively trying to 'debug' the issue for them.
In addition, the tools that Apple has to check the battery is very vague.
When my phone was tested it had a Green/Red/Yellow chart with no axis whatsoever with a dot showing the status of my battery (Green borderline with Yellow). We have tried the phone of my GF, a 2 yrs old iPhone 5S which has completely random battery behaviour. In this case the graph showed only the Yellow square but with no indication of where the battery was in terms of battery life.
Now considering what to do with the iPhone as I am now a bit disappointed by how this (very) high end phone behaved.