So far, I've been using first person in what I write. It gives more immediacy, while third person is more aloof and removed.
There are styles of third person that are anything but aloof and removed, and there are forms of first that can feel pretty formal and retrospective.
I would think first person is comparatively rare. I prefer third because it gives the reader a chance to know all characters equally well...first person is limited to one character's thoughts. Some make up for that by jumping from character to character with each chapter while remaining in first person.
I don't think first person is especially rare. A high percentage of books I've read have been written in first person over the past few years. I read a lot of SF and fantasy, so it may not be the same across all genres and marketing demographics. First person is quite common in books written for teens and for older kids, for instance.
We should beware confirmation bias, though, when making assessments about which narrative approaches are most common. There's a human tendency to notice things that confirm our expectations and to gloss over or dismiss examples that don't.
Both first and third have a variety of narrative depths and styles the author can utilize. I wouldn't say one is more versatile or better than another. It's a matter of deciding how you want (or need) to tell the story you desire.
Other things can be manipulated too, such as making a story in past tense vs present, but even past tense can be manipulated to feel more immediate.
With third, there's the objective vs omniscient vs limited third decision (also decisions about the tone or voice and immersion in narrator versus being more invisible). With first, one gets to decide if the story is epistolary (told via letters or diary entries), or someone reflecting back on events from some time ago, or relating a story that is unfolding now (or a few seconds before). There are also decisions (with omniscient third and with a more reflective first) whether the narrator ever addresses the reader, as if they were in the room telling the reader a story.
Also, if in a character-focused viewpoint, such as first or limited third, one gets to decide if there is a single narrative viewpoint or more.
This is part of the fun of writing.