is the kings gambit better when transposed into from the bishops opening?

Sometimes you can reach a position of the King's Gambit Declined from the Bishop's Opening that's favorable for White, but generally the f4 move in the Bishop's Opening is best done a little later.  The chess engines Stockfish 8 and Houdini 2 both rate White down the equivlent of half a pawn after 3 f4 - assuming Black played the almost automatic 2...Nf6, attacking the White e-Pawn.

A high school team I coached got a lot of success out of 1 e4 e5, 2 Bc4 Nf6 3 d3 Nc6 4 Nc3 then -if Black does NOT play 4...Bc5 - 5 f4! generally works well.  Stockfish 8, looking 20 ply deep, says White is slightly up after 4...e6 5 f4! and no other move is strongly recommended over it.

If Black doesn't immediately exchange, we had good results with 6 f5 where Black's pieces are all blocked to the Q-side and White can put his QN at d5, castle long, and get all his pieces smashing into Black's K-side, led by a f, g, h Pawn charge.

BUT,  if Black gets in that ...Bc5 move, Stockfish and Houdini think f4 puts White behind half a pawn and, we found with that Black B near the center, moves like ...d5, ...Nd4,  ...a6 and ...b5 make a strong counter and White can find his King vulnerable.

So, if Black plays an early Bc5, we'd often go with Nf3 and play a variation of the Giuoco Piano where your pieces are well protected and, while you try to make threatening moves, you're mostly waiting for Black to make a mistake, positionally or tactically.

Note that the Vienna is also an opening in the same group that sometimes transpose into each other.

And what after black plays the usual 1.e4 e5 2.Bc4 Nf6 3.d3 c6    and then goes d5 ?

It can be possible when Black doesn't play an early ...Nf6. I think you're more likely to get some kind of Vienna game with f4 though.

I would play 3. f4 only against 2....Nc6