String#equals()不仅比较这个字符串的内容还检查另一个被比较的对象是否是String类型，String#contentEquals()只比较两者的内容是否相同，不检查被比较对象的类型。

String s = "hello world";
StringBuilder sb = new StringBuilder("hello world");

System.out.println(s.equals(sb));
System.out.println(s.contentEquals(sb));

output：

false
true

看String#equals()方法：

public boolean equals(Object anObject) {
    if (this == anObject) {
        return true;
    }
    //如果不是String继承体系的类相比较，都返回false
    if (anObject instanceof String) {
        String anotherString = (String)anObject;
        int n = value.length;
        if (n == anotherString.value.length) {
            char v1[] = value;
            char v2[] = anotherString.value;
            int i = 0;
            while (n-- != 0) {
                if (v1[i] != v2[i])
                    return false;
                i++;
            }
            return true;
        }
    }
    return false;
}

String#contentEquals()源码，String#contentEquals(StringBuffer sb)和String#contentEquals(CharSequence cs)一样的：

public boolean contentEquals(CharSequence cs) {
    // Argument is a StringBuffer, StringBuilder
    if (cs instanceof AbstractStringBuilder) {
        if (cs instanceof StringBuffer) {
            synchronized(cs) {
               return nonSyncContentEquals((AbstractStringBuilder)cs);
            }
        } else {
            return nonSyncContentEquals((AbstractStringBuilder)cs);
        }
    }
    // Argument is a String
    if (cs instanceof String) {
        return equals(cs);
    }
    // Argument is a generic CharSequence
    char v1[] = value;
    int n = v1.length;
    if (n != cs.length()) {
        return false;
    }
    for (int i = 0; i < n; i++) {
        if (v1[i] != cs.charAt(i)) {
            return false;
        }
    }
    return true;
}

再看nonSyncContentEquals()方法：

private boolean nonSyncContentEquals(AbstractStringBuilder sb) {
    char v1[] = value;
    char v2[] = sb.getValue();
    int n = v1.length;
    if (n != sb.length()) {
        return false;
    }
    for (int i = 0; i < n; i++) {
        if (v1[i] != v2[i]) {
            return false;
        }
    }
    return true;
}

比较String类型与String,StringBuilder, StringBuffer, CharBuffer,等类型内容的相等性使用String#contentEquals()。

参考：

Difference between String#equals and String#contentEquals methods