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C (gcc), 44 bytes

x(o,r)char*o,*r;{*o|*r?*o^=*r,x(o+1,r+1):0;}

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Uses recursion, note that to print strings containing the null byte one will have to manage the strings as arrays. (See the footer of the link for an example)

C (gcc), 50 bytes

x(o,r)char*o,*r;{*o|*r?*o^=*r,x(o+!!*o,r+!!*r):0;}

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Slightly safer version (doesn't read past end of strings, requires enough memory to exist past them though - a la strcpy).

C (gcc), 61 bytes

x(b,o,r)char*b,*o,*r;{*o|*r?*b=*r^*o,x(b+1,o+!!*o,r+!!*r):0;}

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As safe as any standard C function taking a buffer, at the cost of a few more bytes.