Apart from being of the same genre and containing similar enough art style, I don't think the productions are related.
- The authors are different (Masahiro Yokotani vs Haruichi Furudate)
- The production studios are different: Haikyuu!! is produced by Production I.G, Free! by Kyoto Animation
- Haikyuu!! is shonen whilst Free! is mostly targeted at women.
- Character style (but this could just be that the style of the characters has been found to appeal to their target market and chosen for this reason)
- Exclamation marks in their title!! (but so has K-On!! and many other shows)
- Sports genre
The similarities between the shows aren't really substantial enough to warrant a link between them, so I doubt they are.
[I thought that Chihayafuru (another sports title) was similar to Haikyuu!! also, but it also doesn't have anything in common, so I think this is just an art style that sports anime have evolved into]