standard C++ (the language)
Yes the language is full implementation because it uses the gcc compiler that supports. However, I consider the C++ standard to include some of the standard libraries that you expect in most implementations to make code portable and, while these may compile, it makes no sense to do so. We are saying the same thing, I think.
If you are saying that the IDE is not the tool you want to use, then there are a lot of alternatives. I use Visual C++ with the Visual Micro Arduino extensions. Others use the Atmel toolchain. Still others use tools that I have never heard of. Depends on your OS (Windows, Mac or Linux) and what you are used to for other programming. There are also some visual programming tools implemented.
Lots of info for this in the forum. Most of it seems to be in "Other Software Development".