If you use radio waves that travel around the earth, the shortest distance they can travel is πR ≈ 20,000km.
If you use neutrinos that travel through the earth, the shortest distance is 2R ≈ 12,700km.
So the advantage is about 7,300km (or in time units, 25ms ≈ 7,300km / (the speed of light))
If you want a book written by someone who knows some real physics, read The Clockwork Rocket by Greg Egan. He changed one simple law of physics, worked out the consequences for quantum mechanics and relativity, made up some plausible–enough biology, and wrote a series of books in the resulting universe. The characters in the book have to discover or teach each other those laws, so the book is actually a pretty decent way to learn something of the laws of our own universe too. He wrote a huge amount of supplementary material as well, going into all the details. Truly an astounding accomplishment.
> As opposed to how we communicate now globally?
From this interaction I thought you'd missed the point that "send messages through the earth" is something we're currently not doing. Of course you're right that the "if there were a way to reliably detect neutrinos" is doing a lot of work.