The WordPress Export and the WordPress Importer plugin are a good tools and they export and import the most things fine. For instance all post will look like in the old blog also with podPress player and download links at the right places. But the download links and the URLs which the players use will still point to the old location.
In other word you probably need to change the URLs of the media files manually.
The importer imports also only media files which are in the media library of the old blog. As far as you have not uploaded your podcast files with the WP media upload dialog your podcast files are most likely not in that library. But there is a plugin which searches for media files in certain folders of your blog and adds them to the media library automatically. It is called Add From Server.
But often podcast files are relative big files and the WordPress Importer plugin would probably need a lot of time to download and import the podcast files. Maybe this script would need more time than it is allowed by limitation on the server like max_execution_time (which is often not more than 10 minutes). But I don't know whether the WP Importer plugin can handle such time limits or not.
So it is probably no problem to migrate the posts with these tools. The second step would probably be (downloading and) uploading the podcast episodes to the new locations.
The third step would be changing the URLs of the podPress media files in each podcast post.
The WP export and the WP Importer plugin do not export and import the statistic tables (e.g. wp_podpress_stats and wp_podpress_statcounts). But if you have access to the phpMyAdmin interface of your data base (or something comparable) then you can export and import these two tables with the tools of this db web interface. You could probably also use one of the db backup plugins. Maybe there is one which lets you choose the db tables.
But thanks to the circumstance that podPress does not use the full URL to a media file as an identifier for the stats, you probably do not need to change a thing in these tables after the migration if it is your wish to simply continue the counting.
I hope that this helps you a little bit.