If you put all the music you want to add to both in a playlist, you can transfer that playlist, it will copy everything in it to your device and once it is on there you can browse using any of the available sort methods. Thats how I would do it.
To get exactly what you have on the iPhone, on your phone add everything to one playlist, then hook up your iPhone and in iTunes go to "On This Device".
Right Click on the playlist you just made and choose "Export"
When you export it, make it an XML (for some reason m3u wasn't working for me)
Once it is exported go back to your library screen on your computer and choose: File>Library>Import Playlist
Navigate to where you exported the iPhone's playlist and select it for import. As long as all the music on your phone is on your computer too, it will all be added to this playlist, and then you can move all of it at once onto your iPad via the playlist.
