which is gramatically correct.......nowadays..!!!!.

[janzman]

Better of two
Best of three (or more)

Elder of two
Oldest of three (or more)

Faster of two
fastest of three (or more)

Many more examples please

[Ice.Maiden]

Better OF the two.
Best of three - if in context.

Elder OF the two.
Eldest of the three.

Faster OF the two.
Fastest OF the three.

[FoxLee2]

You're talking about comparatives and superlatives. Comparatives refer to two people/objects and end in ER

so taller, shorter, thinner, fatter, happier, sadder, chattier, quieter etc.

Superlatives relate to 3 or more and end in EST

so tallest, thinnest, briefest, sunniest, rainiest, loudest.

more and most are also used for adjectives of two or more syllables so it would be more thoughtful or most beautiful although adjectives with two syllables ending in Y (happy, jolly) still become happier, happiest, jollier, jolliest.

[Canary42]

These are often mis-used. Another example is former and latter which strictly speaking should only be for two. (First and Last for more than two)