You are making some conversions with your Strings that are not necessary. There is a SimpleDateFormat class for it - try this:
SimpleDateFormat myFormat = new SimpleDateFormat("dd MM yyyy");
String inputString1 = "23 01 1997";
String inputString2 = "27 04 1997";
try {
    Date date1 = myFormat.parse(inputString1);
    Date date2 = myFormat.parse(inputString2);
    long diff = date2.getTime() - date1.getTime();
    System.out.println ("Days: " + TimeUnit.DAYS.convert(diff, TimeUnit.MILLISECONDS));
} catch (ParseException e) {
    e.printStackTrace();
}
 Since there have been some discussions regarding the correctness of this code: it does indeed take care of leap years. However, the TimeUnit.DAYS.convert function loses precision since milliseconds are converted to days (see the linked doc for more info). If this is a problem, diff can also be converted by hand:
float days = (diff / (1000*60*60*24));
Note that this is a float value, not necessarily an int.