1.e4 e5 2.Nf3 Nc6 3.d4 exd4 4.Nxd4 Nf6

This is the point where I have a question. The line continues:
5.Nc3 Bb4 6.Nxc6 bxc6 7.Bd3

However, looking at this opening I saw another variation that caught my attention.
5.Nc3 Bb4 6.Nxc6 Bxc3+ 7.bxc3 bxc6

With this variation white's pawn structure is quite weak which made me think this variation is worse. However, the computer engine is telling me that this variation is better for white then the first one.

Can someone help shed some light on the situation?

One difference I see is that white's f1 bishop can be moved anywhere on the diagonal. But he still has to decide how to protect e4. However in the second line he's closer to castling. I think it's a toss up.

In both variations, the f1 bishop is free to move along that diagonal. Also, in the second variation I would still probably play Bd3. What I'm trying to understand is why the computer is giving white a bigger advantage in the second variation even with its weak pawn structure. The only thing I see is that with blacks dark bishop white can protect e4 with f3 and still castle leaving the f1 bishop free to move around.

Also, in order to avoid possible pawn problems I have been looking into this variation.

5. Nxc6 bxc6 6.Bd3 d5 7.e5

If black plays something else turn 6 I could castle and then figure out what to do.

First, use computers only as a reference point, they're not gods at chess they never will be either. Their horizons can wreak havoc on opening analysis.

6. ... bxc6 is the main line here in case you were wondering. On general opening principle, it's the better move. The pawn structure is a non-issue as bxc6 occurs with frequency. It reinforces the necessary d5 break for black by controlling d5, takes away the b5 square for the bishop and knight and black gets to keep a perfectly good bishop; if black doesn't have to exchange he really shouldn't. Black will get in d5, if white then plays e5, Ng4 will be the beginning for a black advantage.

If Bxc3+ first, black loses a bishop in an open game, which is technically bad. A few moves later, white can be comfy if he deviates from the established line with 7. bxc3 bxc6 8. Bd3 d5 9. e5.The advantage of the line without the bishop exchange being a little clearer.

One leads to a positional advantage for white, the other to relative equality when white takes with exd5... Depends on precision play in any case, one not-so-correct move and it'll bounce either way...

Just fYI, a common line here is 5.Nxc6 bxc6 6.e5.

Why Nxd4?
Isn't the goal of the gambit to develop quickly?

Eh, 4. Nxd4 is the Scotch Game, no gambit involved there. 4. Bc4 is the Scotch Gambit, offering a pawn, though various transpositions are possible. The Scotch is perfectly good and has a reputation of playability and solidity. Good opening at all levels.

Oh... I thought the Scotch gambit was also known as the Scotch Game.

Nope two very distinct lines.