No quick and easy way exists, you'll need to compare each individual character in the Strings. Note that Strings themselves never change, they are immutable, but you can compare different Strings.
Here's something I knocked up which will tell you there the first difference is, feel free to adapt it for your needs:
String oldString = "abcdexghijklmn";
String newString = "abcdefghijklm";
//get length of longer string
int end = Math.max(oldString.length(), newString.length());
//loop through strings
for (int position=0; position<end; position++) {
if (position>=newString.length()) {
// Reached the end of new string
System.out.println("Difference at position "+position+" new string is shorter");
break;
} else if (position>=oldString.length()) {
// Reached the end of old string
System.out.println("Difference at position "+position+" new string is longer");
break;
} else {
//compare characters at this position
char newChar = newString.charAt(position);
char oldChar = oldString.charAt(position);
if (newChar!=oldChar) {
System.out.println("Difference at position "+position);
break;
}
}
}