User should be able to move the connection from one panel to another...
Often times we duplicate a connection and then feel handicapped to view content of both the connection side by side. The current option is to launch as a new connection a different panel right from the get go.
The final solution would be to allow drag and drop of the tabs to another panel.
But maybe, as a first step you could add a new entry to the context menu of the tabs like "Move Tab to..." to open the "Select Panel" dialog.
I have been using this workaround for 4+ years : Options->Check "Always show panel selection dialog when opening connections". With this option enabled, if you select "Duplicate Connection" the application will prompt you to pick a panel for the duplicated connection. Click New -> Give a different panel name and you are done. I rarely go beyond 3 panels for all my connections.

Nice trick @kuroburki ! This helps when creating new tabs. But if I already have a tab open, there still is no way to move it to another panel.
I face this issue quite often.. Also when duplicate a connection, there should be a duplicate to a new panel option..
I also would love to see this Enhancement. I've tried the "Always show panel selection dialog when opening connections" option, and can't stand the popup cause 90% of the time it's not needed. Drag/drop or a right-click send-to-panel option would be great.
With the implementation of #155, you can now have side by side tabs within the same connection panel by simply dragging and dropping to the desired docked location. Currently in the develop branch, a 1.77 alpha is expected soon.
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I face this issue quite often.. Also when duplicate a connection, there should be a duplicate to a new panel option..