Note: It seems like this should really be a comment on one of the other answers, or an edit, but I couldn't decide where it fit best.
The length of the time period is not as important as its constancy.
One big benefit of fixed-time Pomodoros is the way you get into a rhythm of work and rest. After you've used the technique for a while, you'll find that you begin to wind up both work and breaks naturally.
Another benefit is planning. If a Pomodoro is a fixed size, you can use it for estimation. Once you know your rate of Pomodori/hour, you'll be able to plan out your work time realistically. I have written a "to do today" list for years, but I usually did not get everything on the list done in a day. This led to me always feeling behind. When I started using the Pomodoro technique, I found that I simply had unrealistic expectations for how much I would get done in a day. Now I'm able to plan a day reliably, and get done what I expect to get done. This is a big deal. I can keep promises to myself and others much better when I have a realistic plan.
Remember the length of a Pomodoro is not designed for you to work to exhaustion, but for you to work productively and also rest enjoyably. It's not just to get the most done; it's to get done what you want, and enjoy the rest of life too.
Perhaps as an aside, I find that the breaks themselves have a huge benefit in keeping me on track. Before I implemented the Pomodoro technique, I would often get "lost" in one of two ways. Either I would get so involved in one task that I'd lose track of time, and then not do other things on my list (losing track of the big picture); or else I'd get distracted by one thing after another, and never go deep on any task (being too scattered). A rhythm of work and rest allows me to dive into a task for a Pomodoro at a time, then come up for air and survey the landscape of the day, so that I can make better decisions about what to do next.
I suspect that this balance of deep focus and broad attention is supported by a predictable rhythm of Pomodoro intervals.