On planes with three classes, first will be better than business - perhaps a little, perhaps a lot. That's the only thing one can state with certainty. (Class names are not standardized. What you refer to as "third" is generally called "coach" or "economy." Some airlines, like BA, have "cutesy" names for the classes.)

Across airlines, there are no standards. One airline's business class may be better than another's first. One airline's first may be better or worse in different markets: AA's domestic F (in all but a few 3-class transcon flights) isn't up to its overseas business class, let alone overseas F. The "business class" seating of most European airlines within Europe - typically economy seats with the armrests shifted toward the middle, to increase seat width a few inches at the window and aisle, and what's left of the middle seat not sold - are nowhere near what they sell as trans-Atlantic business class. To make things more complicated, the same seat may be designated "first class" in some markets, "business class" in others.

Finally, airlines like UA may divide one nominal class into sub-classes with different seating (e.g., more row pitch) or other amenities.

In a competitive market with no universal definitions and everyone looking for a more effective way to do sell, you have to look at each case individually. There are generalizations, but no rules.