The Library of Congress and Writer’s Guild of America only protect the submitted copy. Plus the WGA only “protects for five years if not renewed. Each subsequent revision, no matter how minor, is not protected. That said you must be able to financially defend your ownership. Unless you have deep pockets, all that both methods do is prove the date of authorship OF THE SUBMITTED VERSION.
Should you go the registration route? Most definitely you should register. Just be aware of the limitations.
As the existence of a work in any tangible form is a de facto copyright, I highly recommend creating a novella, graphic novel or short story that is published and listed for sale in one of the many venues. As a copyrighted work you then own the characters and the story. Creation of one of these additional works will provide an additional proof of time line and ownership. Sales or downloads will help the potential financiers visualize market potential as well as create an “easier read”. The time line is harder to prove without a disinterested “Third Party” registration.
With regard the “Studios”. None are likely to steal your product. It’s much cheaper to option and / or buy than incur the ill will and bad PR a story theft would engender. “Coming to America” is an example that comes to mind.
Just a note: DO NOT post copyright notice and / or WGA registration information on any spec script submitted to a contest, reader, agency or analyst. It is a red flag that screams amateur writer. Reputable contests will ask for it on the application but not the title page. In the script world, some form of protection is assumed.