Hello Eladio
"A Comprehensive Grammar of the English language" (by R.Quirk et al) says as follows.
The superlative is often used for a comparison between two persons/things (like #1), but this is avoided in careful usage where the comparative is preferred (like #2).
[1] He is the youngest of the two brother.
[2] He is the younger of the two brother.
I googled "the politest of the two …" but there is not hit for it, although I got 15 hits for "the politer of the two".
The frequency of (careless) use of "the --st of the two" seems dependent on the adjective used. For example, googlily,
The better/best of the two: 443,000/109,000
The smaller/smallest of the two: 414,000/18,100
The bigger/biggest of the two: 52,900/595
"The best of the two" is used in 15 pages against 204 pages for "the better of the two" in The New York Times' domain. The ratio is 54 to 310 in BBC's online pages. So there seems no great regional bias in the choice of "the best or better of the two".
Hope this helps you.
paco