그냥 leftDate.compareTo(rightDate) 하면 되지만, 내부는 이런식으로 되어있음.

LocalDateTime_CompareTo.java

/**
*  날짜 비교 compareTo
*/
public static int compareTo(LocalDateTime leftDate, LocalDateTime rightDate) {
    int cmp = compareDate(leftDate, rightDate); //compare date
    if (cmp == 0) {
        // compare time
        cmp = compareTime(leftDate.toLocalTime(), rightDate.toLocalTime());
    }
    return cmp;
}

// LocalDate의 compareTo0
private static int compareDate(LocalDateTime leftDate, LocalDateTime rightDate) {
    int cmp = leftDate.getYear() - rightDate.getYear();
    if (cmp == 0) {
        cmp = leftDate.getMonthValue() - rightDate.getMonthValue();
        if (cmp == 0) {
            cmp = leftDate.getDayOfMonth() - rightDate.getDayOfMonth();
        }
    }
    return cmp;
}

// LocalTime의 compareTo
private static int compareTime(LocalTime leftTime, LocalTime rightTime) {
    int cmp = Integer.compare(leftTime.getHour(), rightTime.getHour());
    if (cmp == 0) {
        cmp = Integer.compare(leftTime.getMinute(), rightTime.getMinute());
        if (cmp == 0) {
            cmp = Integer.compare(leftTime.getSecond(), rightTime.getSecond());
            if (cmp == 0) {
                cmp = Integer.compare(leftTime.getNano(), rightTime.getNano());
            }
        }
    }
    return cmp;
}