Here's what you can do for say yyyy-mm-dd comparison:
GregorianCalendar gc= new GregorianCalendar();
gc.setTimeInMillis(System.currentTimeMillis());
gc.roll(GregorianCalendar.DAY_OF_MONTH, true);
Date d1 = new Date();
Date d2 = gc.getTime();
SimpleDateFormat sf= new SimpleDateFormat("yyyy-MM-dd");
if(sf.format(d2).hashCode() < sf.format(d1).hashCode())
{
System.out.println("date 2 is less than date 1");
}
else
{
System.out.println("date 2 is equal or greater than date 1");
}