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C, 230 characters

My first golf attempt. Maybe not a hole-in-one, but it works. Not being allowed to use strlen for this forces it to be fairly verbose in C. Maybe it can be shortened a bit?

int a[2],w,i;
int main(int c,char **v){
    for(i=0;(a[0]<256)||(a[1]<256);i++){
        if(!v[1][i])a[0]|=256;
        if(!v[2][i])a[1]|=256;
        if(!(a[0]&256))a[0]++;
        if(!(a[1]&256))a[1]++;
    }
    a[0]&=255;a[1]&=255;
    w=a[0]>a[1]?0:1;
    printf("%s %i\n",v[w+1],a[w]);
}

Example output:

N:\>golf.exe everything works
everything 10