_DEBUG vs NDEBUG

I rely on NDEBUG, because it's the only one whose behavior is standardized across compilers and implementations (see documentation for the standard assert macro). The negative logic is a small readability speedbump, but it's a common idiom you can quickly adapt to.

To rely on something like _DEBUG would be to rely on an implementation detail of a particular compiler and library implementation. Other compilers may or may not choose the same convention.

The third option is to define your own macro for your project, which is quite reasonable. Having your own macro gives you portability across implementations and it allows you to enable or disable your debugging code independently of the assertions. Though, in general, I advise against having different classes of debugging information that are enabled at compile time, as it causes an increase in the number of configurations you have to build (and test) for arguably small benefit.

With any of these options, if you use third party code as part of your project, you'll have to be aware of which convention it uses.

Is NDEBUG standard?

Yes it is a standard macro with the semantic "Not Debug" for C89, C99, C++98, C++2003, C++2011, C++2014 standards. There are no _DEBUG macros in the standards.

C++2003 standard send the reader at "page 326" at "17.4.2.1 Headers" to standard C.

That NDEBUG is similar as This is the same as the Standard C library.

In C89 (C programmers called this standard as standard C) in "4.2 DIAGNOSTICS" section it was said

https://port70.net/~nsz/c/c89/c89-draft.html

If NDEBUG is defined as a macro name at the point in the source file where <assert.h> is included, the assert macro is defined simply as

     #define assert(ignore) ((void)0)

If look at the meaning of _DEBUG macros in Visual Studio https://docs.microsoft.com/en-us/cpp/preprocessor/predefined-macros then it will be seen, that this macro is automatically defined by your сhoice of language runtime library version.

Visual Studio defines _DEBUG when you specify the /MTd or /MDd option, NDEBUG disables standard-C assertions. Use them when appropriate, ie _DEBUG if you want your debugging code to be consistent with the MS CRT debugging techniques and NDEBUG if you want to be consistent with assert().

If you define your own debugging macros (and you don't hack the compiler or C runtime), avoid starting names with an underscore, as these are reserved.