java.time
The java.util Date-Time API and their formatting API, SimpleDateFormat are outdated and error-prone. It is recommended to stop using them completely and switch to the modern Date-Time API*.
Also, quoted below is a notice from the home page of Joda-Time:
Note that from Java SE 8 onwards, users are asked to migrate to java.time (JSR-310) - a core part of the JDK which replaces this project.
Solution using java.time, the modern Date-Time API: Your Date-Time string does not have timezone information and therefore it can be described as a local Date-Time. So, parse it to LocalDateTime and apply the timezone to it to get the ZonedDateTime.
Demo:
import java.time.LocalDateTime;
import java.time.ZoneId;
import java.time.ZonedDateTime;
import java.time.format.DateTimeFormatter;
import java.util.Locale;
public class Main {
    public static void main(String[] args) {
        String defaultSimpleDateFormatPattern = "MMM dd, uuuu HH:mm:ss";
        ZoneId tzNY = ZoneId.of("America/New_York");
        ZoneId tzLos = ZoneId.of("America/Los_Angeles");
        String dateToTest = "Jan 03, 2015 23:59:59";
        DateTimeFormatter dtf = DateTimeFormatter.ofPattern(defaultSimpleDateFormatPattern, Locale.ENGLISH);
        LocalDateTime ldt = LocalDateTime.parse(dateToTest, dtf);
        ZonedDateTime zdtNY = ldt.atZone(tzNY);
        ZonedDateTime zdtLos = ldt.atZone(tzLos);
        System.out.println(zdtNY.isAfter(zdtLos) ? "after" : zdtNY.isBefore(zdtLos) ? "before" : "equal");
    }
}
Output:
before
ONLINE DEMO
Alternatively, Create separate DateTimeFormatter specific to each timezone i.e. ask Java to parse the local Date-Time string applying the given timezone.
Demo:
import java.time.ZoneId;
import java.time.ZonedDateTime;
import java.time.format.DateTimeFormatter;
import java.util.Locale;
public class Main {
    public static void main(String[] args) {
        String defaultSimpleDateFormatPattern = "MMM dd, uuuu HH:mm:ss";
        ZoneId tzNY = ZoneId.of("America/New_York");
        ZoneId tzLos = ZoneId.of("America/Los_Angeles");
        String dateToTest = "Jan 03, 2015 23:59:59";
        DateTimeFormatter dtfNY = DateTimeFormatter.ofPattern(defaultSimpleDateFormatPattern, Locale.ENGLISH)
                                    .withZone(tzNY);
        DateTimeFormatter dtfLos = DateTimeFormatter.ofPattern(defaultSimpleDateFormatPattern, Locale.ENGLISH)
                                    .withZone(tzLos);
        ZonedDateTime zdtNY = ZonedDateTime.parse(dateToTest, dtfNY);
        ZonedDateTime zdtLos = ZonedDateTime.parse(dateToTest, dtfLos);
        System.out.println(zdtNY.isAfter(zdtLos) ? "after" : zdtNY.isBefore(zdtLos) ? "before" : "equal");
    }
}
Output:
before
ONLINE DEMO
Learn more about the modern Date-Time API from Trail: Date Time.
What is wrong with your code?
- You have not set a timezone to your SimpleDateFormat: Unlike the modern Date-Time API with which you have multiple ways to create a Date-Time object specific to a timezone, you have only this way with the legacy API to deal with such a situation (because java.util.Date does not hold timezone information). It is similar to the alternative example shown above.
- You have not set a Localeto yourSimpleDateFormat: Never use SimpleDateFormat or DateTimeFormatter without a Locale. Luckily, your program did not crash because your JVM's timezone must be an English locale.
Demo:
import java.text.ParseException;
import java.text.SimpleDateFormat;
import java.util.Calendar;
import java.util.Locale;
import java.util.TimeZone;
public class Main {
    public static void main(String[] args) throws ParseException {
        String defaultSimpleDateFormatPattern = "MMM dd, yyyy HH:mm:ss";
        TimeZone tzNY = TimeZone.getTimeZone("America/New_York");
        TimeZone tzLos = TimeZone.getTimeZone("America/Los_Angeles");
        String dateToTest = "Jan 03, 2015 23:59:59";
        SimpleDateFormat df = new SimpleDateFormat(defaultSimpleDateFormatPattern, Locale.ENGLISH);
        df.setTimeZone(tzNY);
        Calendar c = Calendar.getInstance();
        c.setTime(df.parse(dateToTest));
        df.setTimeZone(tzLos);
        Calendar c1 = Calendar.getInstance(tzNY);
        c1.setTime(df.parse(dateToTest));
        System.out.println(c.after(c1) ? "after" : (c.before(c1) ? "before" : "equal"));
    }
}
Output:
before
ONLINE DEMO
* For any reason, if you have to stick to Java 6 or Java 7, you can use ThreeTen-Backport which backports most of the java.time functionality to Java 6 & 7. If you are working for an Android project and your Android API level is still not compliant with Java-8, check Java 8+ APIs available through desugaring and How to use ThreeTenABP in Android Project.