1. They were both on the Super Nintendo Entertainment System
2. They were both on the Nintendo 64
3. They were both on the Nintendo GAMECUBE
4. They're both set in a science fiction setting.
5. They both have multiple planets that you visit.
6. They have characters that cross over. StarFox's dad is represented by James McCloud. In the new Star fox game, StarFos Command, Octoman appears as a boss in it.
7. They are both themes for the mafia games we play. Mine is F-Zero. Wandering's will be StarFox.
8. They both have the letter F, O, and R in their titles.
9. Both franchises appear in the Super Smash Bros series.
10. In Super Smash Bros Melee, Starfox has two stages. One is a side view of the great fox and the other is a head-on view of the Great Fox. The F-Zero stages have a side view of a race at Big Blue and a head-on view of a race at Mute City.
11. Takaya Imamura is an artwork designer for Nintendo. He designed the characters from the F-Zero and Star Fox series. He is credited for creating many of the characters, universe, and overall concept of those franchises. He is the original designer of Captain Falcon and Fox in Super Smash Bros.. Imamura is also credited for creating the overall concept of the titles of these series. (quoted from Wikipedia.)