In my opinion, your two best options are
R-Studio and
R-Explorer. Don't let the similar names confuse you, they are from two different companies. I've found that for certain file systems such as Apple HFS+ and FAT32 R-Explorer often gets marginally better results with rebuilding the folder structure. However, for RAW file recovery, R-Studio has an edge, especially since it allows you to create your own custom search headers for unusual file types.
That having been said, if files were deleted some time ago and the drive has been in continued use, don't expect great results. Files that are overwritten with new data can't be recovered by any means. It's simply not possible despite what the conspiracy theorists will tell you.
Regarding your external, did you actually have it evaluated by a data recovery lab? Or, is it just your personal diagnosis that it 'can't be repaired'?