How do I pass a literal double quote from PowerShell to a native command?

You get different behavior, because you're using 4 different echo commands, and in different ways on top of that.

PS> echo '"hello"'
"hello"

echo is PowerShell's Write-Output cmdlet.

This works, because the cmdlet takes the given argument string (the text within the outer set of quotes, i.e. "hello") and prints that string to the success output stream.

PS> c:\cygwin\bin\echo '"hello"'
hello

echo is Cygwin's echo.exe.

This doesn't work, because the double quotes are removed from the argument string (the text within the outer set of quotes, i.e. "hello") when PowerShell calls the external command.

You get the same result if for instance you call echo.vbs '"hello"' with WScript.Echo WScript.Arguments(0) being the content of echo.vbs.

PS> cmd /c 'echo "hello"'
"hello"

echo is CMD's built-in echo command.

This works, because the command string (the text within the outer set of quotes, i.e. echo "hello") is run in CMD, and the built-in echo command preserves the argument's double quotes (running echo "hello" in CMD produces "hello").

PS> bash -c 'echo "hello"'
hello

echo is bash's built-in echo command.

This doesn't work, because the command string (the text within the outer set of quotes, i.e. echo "hello") is run in bash.exe, and its built-in echo command does not preserve the argument's double quotes (running echo "hello" in bash produces hello).

If you want Cygwin's echo to print outer double quotes you need to add an escaped pair of double quotes to your string:

PS> c:\cygwin\bin\echo '"\"hello\""'
"hello"

I would've expected this to work for the bash-builtin echo es well, but for some reason it doesn't:

PS> bash -c 'echo "\"hello\""'
hello

The problem here is that the Windows standard C runtime strips unescaped double quotes out of arguments when parsing the command line. PowerShell passes arguments to native commands by putting double quotes around the arguments, but it doesn't escape any double quotes that are contained in the arguments.

Here's a test program that prints out the arguments it was given using the C stdlib, the 'raw' command line from Windows, and the Windows command line processing (which seems to behave identically to the stdlib):

C:\Temp> type t.c
#include <stdio.h>
#include <windows.h>
#include <ShellAPI.h>

int main(int argc,char **argv){
    int i;
    for(i=0; i < argc; i++) {
        printf("Arg[%d]: %s\n", i, argv[i]);
    }

    LPWSTR *szArglist;
    LPWSTR cmdLine = GetCommandLineW();
    wprintf(L"Command Line: %s\n", cmdLine);
    int nArgs;

    szArglist = CommandLineToArgvW(GetCommandLineW(), &nArgs);
    if( NULL == szArglist )
    {
        wprintf(L"CommandLineToArgvW failed\n");
        return 0;
    }
    else for( i=0; i<nArgs; i++) printf("%d: %ws\n", i, szArglist[i]);

// Free memory allocated for CommandLineToArgvW arguments.

    LocalFree(szArglist);

    return 0;
}

C:\Temp>cl t.c "C:\Program Files (x86)\Windows Kits\8.1\lib\winv6.3\um\x86\shell32.lib"
Microsoft (R) C/C++ Optimizing Compiler Version 18.00.21005.1 for x86
Copyright (C) Microsoft Corporation.  All rights reserved.

t.c
Microsoft (R) Incremental Linker Version 12.00.21005.1
Copyright (C) Microsoft Corporation.  All rights reserved.

/out:t.exe
t.obj
"C:\Program Files (x86)\Windows Kits\8.1\lib\winv6.3\um\x86\shell32.lib"

Running this in cmd we can see that all unescaped quotes are stripped, and spaces only separate arguments when there have been an even number of unescaped quotes:

C:\Temp>t "a"b" "\"escaped\""
Arg[0]: t
Arg[1]: ab "escaped"
Command Line: t  "a"b" "\"escaped\""
0: t
1: ab "escaped"
C:\Temp>t "a"b c"d e"
Arg[0]: t
Arg[1]: ab
Arg[2]: cd e
Command Line: t  "a"b c"d e"
0: t
1: ab
2: cd e

PowerShell behaves a bit differently:

C:\Temp>powershell
Windows PowerShell
Copyright (C) 2012 Microsoft Corporation. All rights reserved.

C:\Temp> .\t 'a"b'
Arg[0]: C:\Temp\t.exe
Arg[1]: ab
Command Line: "C:\Temp\t.exe"  a"b
0: C:\Temp\t.exe
1: ab
C:\Temp> $a = "string with `"double quotes`""
C:\Temp> $a
string with "double quotes"
C:\Temp> .\t $a nospaces
Arg[0]: C:\Temp\t.exe
Arg[1]: string with double
Arg[2]: quotes
Arg[3]: nospaces
Command Line: "C:\Temp\t.exe"  "string with "double quotes"" nospaces
0: C:\Temp\t.exe
1: string with double
2: quotes
3: nospaces

In PowerShell, any argument that contains spaces is enclosed in double quotes. Also the command itself gets quotes even when there aren't any spaces. Other arguments aren't quoted even if they include punctuation such as double quotes, and and I think this is a bug PowerShell doesn't escape any double quotes that appear inside the arguments.

In case you're wondering (I was), PowerShell doesn't even bother to quote arguments that contain newlines, but neither does the argument processing consider newlines as whitespace:

C:\Temp> $a = @"
>> a
>> b
>> "@
>>
C:\Temp> .\t $a
Arg[0]: C:\Temp\t.exe
Arg[1]: a
b
Command Line: "C:\Temp\t.exe"  a
b
0: C:\Temp\t.exe
1: a
b

The only option since PowerShell doesn't escape the quotes for you seems to be to do it yourself:

C:\Temp> .\t 'BEGIN {print "hello"}'.replace('"','\"')
Arg[0]: C:\Temp\t.exe
Arg[1]: BEGIN {print "hello"}
Command Line: "C:\Temp\t.exe"  "BEGIN {print \"hello\"}"
0: C:\Temp\t.exe
1: BEGIN {print "hello"}

To avoid doing that every time, you can define a simple function:

C:\Temp> function run-native($command) { & $command $args.replace('\','\\').replace('"','\"') }

C:\Temp> run-native .\t 'BEGIN {print "hello"}' 'And "another"'
Arg[0]: C:\Temp\t.exe
Arg[1]: BEGIN {print "hello"}
Arg[2]: And "another"
Command Line: "C:\Temp\t.exe"  "BEGIN {print \"hello\"}" "And \"another\""
0: C:\Temp\t.exe
1: BEGIN {print "hello"}
2: And "another"

N.B. You have to escape backslashes as well as double quotes otherwise this doesn't work (this doesn't work, see further edit below):

C:\Temp> run-native .\t 'BEGIN {print "hello"}' 'And \"another\"'
Arg[0]: C:\Temp\t.exe
Arg[1]: BEGIN {print "hello"}
Arg[2]: And \"another\"
Command Line: "C:\Temp\t.exe"  "B EGIN {print \"hello\"}" "And \\\"another\\\""
0: C:\Temp\t.exe
1: BEGIN {print "hello"}
2: And \"another\"

Another edit: Backslash and quote handling in the Microsoft universe is even weirder than I realised. Eventually I had to go and read the C stdlib sources to find out how they interpret backslashes and quotes:

/* Rules: 2N backslashes + " ==> N backslashes and begin/end quote
          2N+1 backslashes + " ==> N backslashes + literal "
           N backslashes ==> N backslashes */

So that means run-native should be:

function run-native($command) { & $command ($args -replace'(\\*)"','$1$1\"') }

and all backslashes and quotes will survive the command line processing. Or if you want to run a specific command:

filter awk() { $_ | awk.exe ($args -replace'(\\*)"','$1$1\"') }

(Updated following @jhclark's comment: it needs to be a filter to allow piping into stdin.)