Correct, they weren't exactly friends, but they weren't exactly rivals either; their television alter-egos may have always been the best-of-friends, but off camera, their real-life personalities didn't really click too well. Apparently, Vivian even once said "I'm going to have to learn to love that b!+c#"
And for the record, Vivian Vance and William Frawley actually hated each other in real life as well, Frawley apparently has said that Vivian's voice annoyed him more than anything else in the world.