In general using the Features module is the best way to push configuration changes like "Image Styles" from dev to production: http://drupal.org/project/features . Yours is a different use case since you are pushing the entire database.
There is no "good" reason why the Image Styles shouldn't work on your new server. I would check to make sure that the file permissions on your production server are setup correctly. See: http://drupal.org/node/244924
Even if "sites/default/files" is given the proper permissions "sites/default/files/styles" might not have the proper permissions. You can check that the Image Style settings for your server are working correctly by visiting "/admin/config/media/image-styles/edit/thumbnail". If a style is not being generated there is an issue with your server setup.
Are you using 'GD2' or 'ImageMagic' and what version of PHP are you using to resize your images? These are PHP libraries that Drupal needs (1 of them has to be installed) to resize images. If you visit 'admin/reports/status' you should be able to see if one or both are installed correctly.