Neither is lightfast. "Permanent" means not soluble in water. What you want is "archival" which means it can resist light fading for 100 years or more. If you are really interested in the long-term viability of an autograph and you can control the pen that the signer uses, the Sakura Pigma Micron line is archival.
http://www.sakuraofamerica.com/Pen-Archival
If you can get something signed in pencil, an art pencil conforming to ASTM lightfastness standards is best. The American Society for Testing and Material has developed standard ASTM D-6901 to determine the lightfast level of a color pencil. Luminance 6901 by Caran d’Ache offers a set of 76 colors with 61 colors classified in the best category (Lightfastness I) under standard ASTM D-6901.
A black ballpoint will fade to yellow very quickly, especially if the item is displayed under fluorescent lighting. I have a Nolan Ryan signed baseball in my office that was on display for a few years and that faded to yellow very fast. I can no longer display it. My uncle has a photo autographed by Groucho Marx in ballpoint where the ink is completely gone leaving only the impression of the writing.