Theres a number of Firefly references in the game. Its similar in setting to start, space pirates and what not, kinda a steam punk feel, but eridium rather than steam.
Specifically theres a quest early on that is named similar to a line in firefly, cant think of it right off right now. And one of Zero's outfits is "Leaf on the Wind". Tudyuk's last line in the movie Serenity as he crash lands the the ship on the Reaver planet.
None of the characters are alike (seriously, not one), and the Serenity's crew always seemed less infinitely BA. In Borderlands you know you're the most murdertastic and pimptacular thing on the planet, in Firefly they're one bad scrape away from death, fighting/running from a power they can't possibly hope to beat.
Sure there's a bit of the Western-in-Space feel, but they go about it in such completely different ways I just can't relate the two.