Better and First-rate

Better adjective - (comparative of `good') superior to another (of the same class or set or kind) in excellence or quality or desirability or suitability; more highly skilled than another.

First-rate and better are semantically related. In some cases you can use "First-rate" instead an adjective "Better".

First-rate adjective - Of the very best kind.

Better and first-rate are semantically related. Sometimes you can use "Better" instead an adjective phrase "First-rate".