+1 to Gui13 for providing a link to the source of gcc stdlib strcmp (http://sourceware.org/git/?p=glibc.git;a=blob;f=string/strcmp.c;h=bd53c05c6e21130b091bd75c3fc93872dd71fe4b;hb=HEAD)!
You are correct that strcmp can never be faster than a direct comparison[1], but the question is, will the compiler optimise it? I was intimidated to try measuring that, but I was pleasantly surprised at how easy it was. My sample code is (omitting headers):
bool isEmpty(char * str) {
   return 0==std::strcmp(str,"");
}
bool isEmpty2(char * str) {
   return str[0]==0;
}
And I tried compiling that, first with gcc -S -o- emptystrcmptest.cc and then with gcc -S -O2 -o- emptystrcmptest.cc. To my pleasant surprise, although I can't read the assembly very well, the non-optimised version clearly showed a difference, and the optimised version clearly showed the two functions produced identical assembly.
So, I would say that in general, there's no point worrying about this level of optimisation.
If you are using a compiler for an embedded system and know it not to handle this sort of simple optimisation (or don't have a standard library at all), use the hand-coded special-case version.
If you are coding normally, use the more readable version (imho that may be strcmp or strlen or [0]==0 depending on context).
If you are writing highly efficient code you expect to be called thousands or millions of times a second, (a) test which is actually more efficient and (b) if the readable version is actually too slow, try to write somethign which will compile to better assembly.
With gcc -S -o- emptystrcmptest.cc:
            .file   "emptystrcmptest.cc"
            .section .rdata,"dr"
    LC0:
            .ascii "\0"
            .text
            .align 2
    .globl __Z7isEmptyPc
            .def    __Z7isEmptyPc;  .scl    2;      .type   32;     .endef
    __Z7isEmptyPc:
            pushl   %ebp
            movl    %esp, %ebp
            subl    $24, %esp
            movl    $LC0, 4(%esp)
            movl    8(%ebp), %eax
            movl    %eax, (%esp)
            call    _strcmp
            movl    %eax, -4(%ebp)
            cmpl    $0, -4(%ebp)
            sete    %al
            movzbl  %al, %eax
            movl    %eax, -4(%ebp)
            movl    -4(%ebp), %eax
            leave
            ret
            .align 2
    .globl __Z8isEmpty2Pc
            .def    __Z8isEmpty2Pc; .scl    2;      .type   32;     .endef
    __Z8isEmpty2Pc:
            pushl   %ebp
            movl    %esp, %ebp
            movl    8(%ebp), %eax
            cmpb    $0, (%eax)
            sete    %al
            movzbl  %al, %eax
            popl    %ebp
            ret
    emptystrcmptest.cc:10:2: warning: no newline at end of file
            .def    _strcmp;        .scl    2;      .type   32;     .endef
With gcc -S -O2 -o- emptystrcmptest.cc:
        .file   "emptystrcmptest.cc"
emptystrcmptest.cc:10:2: warning: no newline at end of file
        .text
        .align 2
        .p2align 4,,15
.globl __Z7isEmptyPc
        .def    __Z7isEmptyPc;  .scl    2;      .type   32;     .endef
__Z7isEmptyPc:
        pushl   %ebp
        movl    %esp, %ebp
        movl    8(%ebp), %eax
        popl    %ebp
        cmpb    $0, (%eax)
        sete    %al
        movzbl  %al, %eax
        ret
        .align 2
        .p2align 4,,15
.globl __Z8isEmpty2Pc
        .def    __Z8isEmpty2Pc; .scl    2;      .type   32;     .endef
__Z8isEmpty2Pc:
        pushl   %ebp
        movl    %esp, %ebp
        movl    8(%ebp), %eax
        popl    %ebp
        cmpb    $0, (%eax)
        sete    %al
        movzbl  %al, %eax
        ret
[1] Although be careful -- in cases any more complicated than a direct test against zero, the library and compiler code a typically WILL be better than hand-crafted code.