I am using Eclipse CDT 3.8.1 with GCC Cross Compiler 8.6.0. I know how to change the C++ standard in the project properties, but I don't know what standard is used by default.
I know the default is not C++11 and the Eclipse language support page doesn't mention C++03, so I suspect the default is C++98. However, Eclipse CDT must support C++03 because adding the compiler flag -std=c++03 doesn't cause any errors. https://www.eclipse.org/community/eclipse_newsletter/2017/april/article3.php
What is the default standard when I create a new project?
Eclipse's parser itself doesn't have a notion of a C++ standard mode. It will recognize all the C++ features that have been implemented in its parser (which, as of writing this, is all C++98 and C++11 features, some (but not all) C++14 features, and a handful of C++17 features).
However, standard library headers often contain sections that are conditional on macros denoting the C++ standard version (e.g. #if __cplusplus >= 201103 is a common check for "C++11 or later"). To determine the value of these macros, Eclipse invokes the compiler specified in the project's toolchain to discover built-in macros. The discovered value of e.g. the __cplusplus macro will depend on what standards mode the compiler runs in for this invocation.
The flags to this compiler invocation are specified in the project properties, as you mentioned. If you don't provide a flag there, the compiler will use whatever its default mode is. I believe GCC has been using -std=c++14 as the default from GCC 6 onwards. (Though I don't quite know what "GCC Cross Compiler 8.6.0" is. According to the GCC website, the latest version is 8.1.)