If you are applying to several different schools using one generic statement will be easily recognized and just as easily dismissed. WHY _ because you will be seen as not making an effort sell yourself to this particular school, low effort equals low interest to admissions representatives. Remember the admission committee will likely view thousands of these statements from qualified candidates and they will spot a weakness, flaw or lack of attention to the process in a heartbeat. What you don't want to do is give this committee an easy excuse to dismiss your statement and application.
The personal statement is also a great place to explain more serious problems, like less_than_ideal grades or test scores. Don't be afraid to write something like, "I don't test well" in the statement. As long as you can provide a good reason for you app's problems, it's okay to address them directly. You won't be able to hide it from admissions officers anyway, so providing a reason for problems is always preferable to ignoring them.