If you just want to compare the date part, you can do it like so:
LocalDate startDate = new LocalDate(2014, 1, 2);
LocalDateTime startDateTime = new LocalDateTime(2014, 1, 2, 14, 0);
LocalDate forCompare = startDateTime.toLocalDate();
System.out.println("equal dates: " + forCompare.equals(startDate));
// equal dates: true