"Binds us together" has a slightly possessive connotation to it that "unites us" doesn't. "Binds us" sounds like two people tied together whereas "unites" sounds like two people being part of a whole.
By the way, Sam, "We have such a love that __________ us" is rather awkward-sounding because of the use of "such". In fact, I'm reasonably certain that it's not grammatically correct. The use of "such" would sound fine in:
"We have such a love that we will be together forever" OR
"We have such a love that nothing will ever split us up"
"Such" is used as an emphasis and it's not working in your sentence.