The Pi Manifesto claims that the Tau Manifesto contains selection bias and uses that as its main argument against the Tau Manifesto's validity, even going so far as to say that the Tau Manifesto is "wrong" because of it. However the Tau Manifesto does not ignore formulas that are simpler with pi as the Pi Manifesto claims; it addresses area of a circle, which is even its coup de grace. What's even worse, though, is that the Pi Manifesto is absolutely loaded with selection bias, containing much more of it than the Tau Manifesto, so its claims are extremely hypocritical.
1. The Pi Manifesto talks about the area of a circle over and over again because it's the only good argument for pi, but this argument was already preemptively refuted by the Tau Manifesto. The Pi Manifesto ignores most of the Tau Manifesto's rebuttal of this argument, only briefly mentioning the connection to other quadratic forms, which was only a small part of the Tau Manifesto's area of a circle argument.
2. The Pi Manifesto completely brushes over the Tau Manifesto's main point on radian angle measure and pretends it isn't important. Radian angle measure is used throughout mathematics, especially in trigonometry, and circular area is used very rarely, but the Pi Manifesto pretends they are of equal importance.
3. nsin(π/n)cos(π/n) is "clearly a win for pi," really? I think you mean 1/2 n sin(τ/n) is clearly a win for tau.
4. The Pi Manifesto mentions interior angles of a polygon but never mentions exterior angles, which always sum to tau, and the formula for the sum of interior angles simplifies to nπ-τ, which is equally simple with either constant, making it a marginal win for pi at best.
5. The Pi Manifesto mentions the zeroes and undefined values of trig functions because they occur twice every period, but it doesn't mention other special values.
6. The quotes from mathematicians in favor of pi were cherry-picked. There are also quotes in favor of tau.
7. In the section on Euler's identity, the Pi Manifesto just conveniently asks a question with pi as the answer. We could also ask "What is the smallest possible positive solution so that e^ix is a positive number or so that it is a natural number?" or "What is the period of e^ix?" or "What value of e^ix corresponds to a full rotation in the complex plane and gets you back where you started?" or "What is the first positive value of e^ix that is equal to one?" The answer to all of these questions is tau. In fact, pi is sometimes defined using that last question and then dividing by 2.
8. The list of "well-known" formulas is extremely cherry-picked. I would also say that, with the exception of the gamma function, none of them are as well-known as the Tau Manifesto's examples. Here's a list of common formulas which is not as selectively chosen. Some are simpler with tau, some with pi, some with eta, and some with neither, but the overwhelming majority are simpler with tau: http://www.harremoes.dk/Peter/Undervis/ ... page1.html
9. The Pi Manifesto cherry-picks definitions that are simpler with pi, but in reality, many of the definitions of pi involve multiplying by 1/2 at the end: https://en.wikipedia.org/wiki/Pi, and there are also other definitions of tau.