Support

I don't understand the difference between "Site Transfer Wizard" and "Backup with Upload to Remote FTP". I think i have no effectable limits or restrictions on my server. So where could be the problem?

Upload to Remote FTP is a post-processing engine. After the backup is complete, Akeeba Backup connects to your remote FTP server and uploads one backup part at a time. You can also copy Kickstart if you check that box in Akeeba Backup's Configuration page. The downside is that if you try to upload a large file (typically over 10Mb, depends on your web server where the backup is running, the remote FTP server and the transfer speed between them) you can run into a timeout error and the transfer will fail.

Site Transfer Wizard (STW), on the other hand, works separately from the backup. It needs a backup to have already been taken. First it uses FTP or SFTP to upload Kickstart itself to the remote server, along with an add-on Kickstart feature. The add-on feature allows Kickstart to operate as an uploads manager. Then STW will send a POST request to the remote copy of Kickstart with an 1Mb chunk of the backup archive. The remote copy of Kickstart will put it in a temporary directory. When all 1Mb chunks of a backup part have been received, the remote copy of Kickstart will assemble the part file and store it alongside kickstart.php. Rinse and repeat for all archive parts and now you have your backup on the remote server, circumventing the large upload issue of Upload to Remote FTP.

The problem is that not all web servers will allow you to use this method. Some servers apply limits on how much data you can upload, or filter POST requests, or don't like uploads not originating from browsers, or... You get the idea. This is what happens in your case. The remote server does not like STW's method of safely uploading files. Therefore using Upload to Remote FTP is the best option at your disposal.

I just bought the PRO version today because of the Site Transfer Wizard, and now exactly this is not working. It's a bit of frustrating...

I think you have it backwards. STW is available in both Core and Pro versions. Upload to Remote FTP, though, is only available in Akeeba Backup Professional. So what you bought actually allows you to transfer the site, whereas using the Core version wouldn't (because of your server's issues).

In fact, if you use the Upload to Remote FTP with the Upload Kickstart option enabled you have the identical functionality of Site Transfer Wizard. After all, STW's job is to upload the backup archive and Kickstart to the remote server.

As I tried to explain, there are two different ways to accomplish that (STW and Upload to Remote FTP/SFTP) because not all servers are compatible with just one of these methods. Most servers support both. Quite a few servers only work with the STW. A few other servers (like yours) only work with Upload to Remote FTP. And yes, there are very very few servers which don't work with anything and are a pain to manage anyway - but there's nothing we can do about that.

Overall, I think you are on the right track with the self-administered solution to your problem. You are using the correct Pro-only feature to perform a site transfer.

I'm glad I could help clarify the differences between these methods :)