what is the best gambit for a development advantage?


He wasn't asking if it "wins every time". The danish gambit is the best for a developmental advantage.

See: Lesson 4 - Advantage in Development
An advantage in development is quite easy to spot - you will have more pieces out than your opponent.

To zBorris. Actually the Kings gambit is only classified as 1. e4 e5 2. f4. The position you showed was the Kings gambit Knights variation. Also, the Danish gambit is only classified as 1. e4 e5 2. d4 exd4 3. c3. Finally, the Kings gambit can usually bring out a ton of pieces in many of its variations. The Danish gambit can be refuted with 1. e4 e5 2. d4 exd5 3. c3 d5!

To zBorris. Actually the Kings gambit is only classified as 1. e4 e5 2. f4. The position you showed was the Kings gambit Knights variation. Also, the Danish gambit is only classified as 1. e4 e5 2. d4 exd4 3. c3. Finally, the Kings gambit can usually bring out a ton of pieces in many of its variations. The Danish gambit can be refuted with 1. e4 e5 2. d4 exd5 3. c3 d5!
Gotta think outside the box a little bit. Per Mega Database 2015 3.Nf3 has been played 12684 times, with 3.Bc4 having been played 3053 times. And what he showed is clearly the main line of the Danish Gambit.

He asked what openings are best for a developmental advantage. After 3...d5, black can get nice development for his peices by giving back a pawn. You are right that 3...d5 does not outright refute the gambit, but because we are trying to look for ways for white to get a huge developmental advantage, the position after 3...d5 gives black easy development to counter whites. Thus in this case I said 3...d5 refuted the gambit.
In almost all lines of the Kings Gambit, white can grab a huge developmental advantage, which can be later used for a deadly attack on the black King. Even though many lines in the Kings Gambit lead to equality or even an advantage for black, white still gets many of his peices out and ready to attack.

In almost all lines of the Kings Gambit, white can grab a huge developmental advantage, which can be later used for a deadly attack on the black King.
Yes of course, that is why all the super GMs are using it.