I prefer to have my fabric torn. If you are getting a geometric print or plaid it reveals how crooked the printing was etc. It does make a difference in quilting. If you have wavy borders it might just be because the fabric is off grain. If I am making strips for peicing I always tear the fabric it is the only way I can get a long strip without having that fold bump in it. I know that the strings are a pain but it does make a difference.