Depends. The body creates antibodies towards more or less specific parts of surface molecules, the antigens. Now if your body manages to create antibodies that are found on both pathogens, they will both be subjected to the immune respone. There are antibodies more specific, so only a certain type of antigen can be adhered to, while other antibodies will attach to almost anything.

Now if person A develops antibodies that have a higher affinity to a antigen than person B, theirs will be more effective at binding pathogens. But there are so many more parameters to check that this alone is not enough to effectively fend off illnesses.