I assume you're wondering how using Settings.Secure.LOCATION_PROVIDERS_ALLOWED, which is depricated in API level 19, is different from using Settings.Secure.LOCATION_MODE, which was introduced in API level 19.
With Settings.Secure.LOCATION_MODE, you have these values (you probably already know this):
LOCATION_MODE_HIGH_ACCURACY, LOCATION_MODE_SENSORS_ONLY,
  LOCATION_MODE_BATTERY_SAVING, or LOCATION_MODE_OFF
You can map these values to Settings.Secure.LOCATION_PROVIDERS_ALLOWED in this way:
LOCATION_MODE_HIGH_ACCURACY : "gps,network"
LOCATION_MODE_SENSORS_ONLY : "gps"
LOCATION_MODE_BATTERY_SAVING : "network"
LOCATION_MODE_OFF : ""
Note that in code, it's best to reference constants LocationManager.GPS_PROVIDER and LocationManager.NETWORK_PROVIDER instead of just "gps" and "network".
Using this answer as a reference, you could do something like this:
public static int getLocationMode(Context context) {
    int locationMode = 0;
    String locationProviders;
    if (Build.VERSION.SDK_INT >= Build.VERSION_CODES.KITKAT) {
        try {
            locationMode = Settings.Secure.getInt(context.getContentResolver(), Settings.Secure.LOCATION_MODE);
        } catch (SettingNotFoundException e) {
            e.printStackTrace();
        }
    } else {
        locationProviders = Settings.Secure.getString(context.getContentResolver(), Settings.Secure.LOCATION_PROVIDERS_ALLOWED);
        if (TextUtils.isEmpty(locationProviders)) {
          locationMode = Settings.Secure.LOCATION_MODE_OFF;
        }
        else if (locationProviders.contains(LocationManager.GPS_PROVIDER) && locationProviders.contains(LocationManager.NETWORK_PROVIDER)) {
          locationMode = Settings.Secure.LOCATION_MODE_HIGH_ACCURACY;
        }
        else if (locationProviders.contains(LocationManager.GPS_PROVIDER)) {
           locationMode = Settings.Secure.LOCATION_MODE_SENSORS_ONLY;
        }
        else if (locationProviders.contains(LocationManager.NETWORK_PROVIDER)) {
           locationMode = Settings.Secure.LOCATION_MODE_BATTERY_SAVING;
        }
    }
    return locationMode;
}