Does migrating to Apple's new Photos app actually double my storage requirements?
Short answer, no. The measuring tool you are using doesn't take the time to deduct the space saved when files are hard linked, so it over-counts the space used.

The Libraries are using 'hard links' to the real location of the files, so both appear to be approximately the same size, but each actual photo is only located in one place on your hard drive, with pointers from both Libraries.

Deleting either Library will not affect the storage space, only deleting both would actually remove the 50GB of data from your drive.

See: Photos saves disk space by sharing images with your iPhoto or Aperture libraries

More on hard links from Ars Technica:


  A hard link is simply a reference to some data on disk. Think of a file as a combination of a name and a pointer to some data. Deleting a file really means deleting the name portion of that duo. When there are no more names pointing to a particular piece of data disk, then that disk space can be reused."