What do you mean by "Is it superior to mingw-w64 in some way?". This command will use mingw headers and libraries, which are also part of mingw-w64. So you are using same stuff (includes/libs) as mingw-w64 would do. Just on Linux, not Windows.
Are there any differences between an exe compiled this way and, say, an exe compiled in Windows with cl?
As a end result - no difference really. It will work & run the same. Obviously there are differences in compilers, so once code may run a bit slower than other compiler, or be smaller that with other compiler. It depends on actual code.
There is really no resource to describe what are actual differences. All you can do is try same code with both and compare results. On low-level you can check disassembly in godbolt - it can display output from multiple compilers, including gcc, clang and MSVC.
What "arcane shit" are you talking about? Those arguments are pretty standard stuff for clang and lld. Just do clang --help or lld --help and you'll get a lot of information on what is possible.
Cross-debugger is called remote debugger. Most debuggers, including Visual Studio and gdb, and lldb, support debugging process remotely. The problem is not the debugger. The problem is how you will run exe on Linux (without debugger). Wine is one option. Virtual Machines are another, but much heavier option. If you are switching to clang & lld, then it kind of makes sense to use their lldb debugger, which should be able to debug Windows binaries running under wine. It's all possible, but from time to time you'll get to something that does not work quite correctly (or is not implemented fully) - as not many people needs this kind of functionality. Be aware.