Since “better” is so subjective, let me rephrase your question: “Which of the two books encapsulates Ayn Rand‘s worldview and delivers her point more wholly?” Atlas Shrugged. (Disclaimer: this is my favorite book; I’ve read it three times. Though I have read The Fountainhead also, once.)
First of all, both books say exactly the same thing, have exactly the same theme, and are about of equal length. So, what’s the difference? The Fountainhead focuses on a single protagonist, Howard Roark, as he struggles to succeed as an individualist. There are only a handful of main characters. The “big monologue” comes toward the end in a court case scene, but I won’t say more to spoil that. Atlas Shrugged spans years of time and focuses on a huge group of protagonists represented in the book as genius industrial innovators. There are literally hundreds of characters to keep up with, but they all fall into very few well-defined classes, so it’s not too difficult to keep track. She called these classes “prime movers” and “moochers” although there are shades of grey, specifically characters I would classify as “the wretched” or “the fallen.” The “big monologue” comes toward the end as a radio broadcast from John Galt. In both, the “big monologue” is kind of the kernel of ideas, much like a college thesis embedded in the novel.
While The Fountainhead was inspired by the life and work of Frank Lloyd Wright and his “form follows function” post-modernist architectural style, Atlas Shrugged feels more like a social science fiction. Much like George Orwell did in 1984, Ayn Rand takes the world that she knew (specifically 1950s McCarthyism) and attempts to push it forward by a couple of decades. She takes the complex political question of communism vs capitalism and frames it simply as a social “good vs evil” struggle. Though she sets both novels in New York City, The Fountainhead never leaves NYC, while Atlas Shrugged is a story that spans the entire U.S., specifically Colorado and Washington D.C., and also Mexico (there is even a “pirate on the high seas” character).
Most importantly, Ayn Rand would probably tell you the same thing. Look at the progression of her work: 1936 We the Living is a semi-autobiographical account of a young woman growing up in the worsening conditions of Soviet Russia. The American public, increasingly warming to the concept of communism (particularly the burgeoning, left-leaning movie industry), rejected it as propagandist. 1938 Anthem was a short sci-fi novella about a human race in the distant future so collectivized that the society took on a form akin to an ant colony, where people had lost the faculty of recognizing themselves as an individual body apart from society. 1943 The Fountainhead expanded this idea into a full-fledged, well-crafted, novel-length story set in the present day. According to Rand, she began journaling Atlas Shrugged the moment she finished The Fountainhead, because she envisioned a much grander stage upon which to set her story. In 1957 she achieved this, delivering another full-length novel, Atlas Shrugged, with exactly the same theme, though an order of magnitude greater in scope, clarity, and power. Then she stopped writing fiction. For the remainder of her days, until her death in 1982, she wrote prolifically on her worldview in the form of non-fiction philosophic treatises. From her own point of view, she had accomplished her lifelong quest to produce her masterpiece, that seminal work that summed up her ideology for posterity.
This places her in the ranks of a very small subclass of artists like Robert M. Pirsig and Harper Lee, who, upon finishing what they believed to be their masterpiece and receiving the critical acclaim they desired, retired from writing fiction. They had something to say, they said it, and that was the end of it. Ayn Rand strikes me as one who grew up in ideological and economic poverty, came to this country and worried it was going in the same direction, and dedicated her life to correcting public opinion on the matter. Although the U.S. left’s sentiment for communism would not wane until the collapse of the USSR in 1991, I believe she played a prominent role in speaking out against it and preserving our more historically capitalist ideals. I once heard a quote that went something like “An artist is a lover of art who sees a void in the art world and feels compelled to fill it.” In that sense, she was an artist, through and through.
By all means, read all of her books, but know that her ideas crystallized as she got older and thus each of her books was “better” than the one before it. (Also, as an aside, the 1949 movie The Fountainhead with Patricia Neal and Gary Cooper is masterful (despite the cheeky trailer), in part because Ayn Rand wrote the screenplay. The recent Atlas Shrugged movies were terrible (despite the very good trailers).)
So, if you’ve heard a lot about her or her books and are looking to see for yourself what she’s all about, that’s my recommendation. Why anyone would voluntarily sit down and read a fifteen hundred page book is a tough question to answer. I hate long books. But, contradiction that I am, Atlas Shrugged is not just my favorite long book, it’s among my favorite, most influential books I’ve ever read. It’s one of those rare long books where every page is engaging, and it’s difficult to imagine cutting it down without sacrificing its quality.