Gerwig, 36, and Baumbach, 50, gave insight into their personal and professional relationship in the Dec. 13 issue of The Hollywood Reporter.
Meanwhile, Baumbach's film Marriage Story debuted Dec. 6 on Netflix. The movie, starring Scarlett Johansson and Adam Driver, is up for six Golden Globe awards, including Best Motion Picture.
When asked about their professional rivalry, Gerwig said it's "exciting" for Little Women and Marriage Story to both be nominated for awards.
"It's exciting to have mutual acknowledgement of the work that he and I have both put into [our movies]," Gerwig said. "There is a sense of wanting to show off for eeach other. At least on my part."
"I remember when I showed Noah cuts or drafts of Little Women. He's my favorite filmmaker and my favorite writer. It means everything to me that he thinks it's good," she added.
Baumbach confirmed that he and Gerwig are involved in each other's creative processes.
"When we're working on our own projects, we're always talking about them and showing each other things. I always feel very much a part of what she's done," Baumbach said.
"[Little Women] is absolutely hers, but it's not like I woke up one day and this movie's in theaters. She's been talking about it for a few years. It feels like, 'How great that this is being recognized in the way that you hoped it would,'" he added.
In addition, Gerwig and Baumbach said they share an understanding of how demanding life as a writer, director and producer can be.
"You come home at 3 in the morning and you climb into bed and the other person's half asleep -- you feel ... Wrecked and lonely and you don't even know if you got [the best footage]," Baumbach said.
"The thing you want more than anything is for someone to just take care of you because shooting a movie is so much," Gerwig added. "But because we're both doing it, we haven't necessarily always been able to be the person who was there. Sometime's it's not completely possible."
Gerwig and Baumbach started dating in 2011 and have co-written the films Frances Ha (2012) and Mistress America (2015). Gerwig said in the January issue of Vogue that she was "frustrated" by critics calling her Baumbach's muse, rather than his co-writer, following the release of Frances Ha.