Danish Gambit

I was wondering with the danish gambit would it be better to capture with Nb3 instead of moving the light colored bishop?

I kinda got this idea from the Smith Morra Gambit and do not see a reason to not use for this one too.

I have tried this before and won (please ignore my ELO) against people ELO's higher than previously

I like the Smith Morra too. I have tried playing it against 1. ... e5 like you show. It didn't work out well for me. In the Morra, black spends their first three turns moving and trading off the c-pawn. This doesn't help get their pieces out at all. Meanwhile White is down a a pawn, but has a nice head start in development.

In the position you show, it's the e-pawn that Black has given up. What's the difference? Now the black bishop on f8 can easily get out. Then black knight to f6, followed by a quick castle, and Black is sitting pretty. Meanwhile White is still down a pawn. Things go down hill from there as White. At least that's how it went for me.

@1

That is not new. Here is a correspondence game:

I feel that your move is the better practical move of the two. Okay, it might not turn out well in correspondence chess (more time to think = fewer tactical errors from the defending side) or against accomplished material-grabbers like the late Viktor Korchnoi in classical chess, but it offers White flexible development and open lines and easy-to-find moves and variety of plan using the initial space advantage. Against woodpushers like Yours Truly or at faster time limits I believe it's the way to go.

In honesty part of this is negative reasoning because Karl Schelchter's old defence line against 4.Bc4 is easy for players of the Black pieces to learn by rote and seems to leave Black at least equal and with a fairly easy position to play in practice. Whereas after 4. Nxc3 Black has no one learnable forcing line to counter White's play and is thrown back on his/her own wit. Health Warning: I'm coming back to chess after a very long layoff: my opening knoweldge might well not be up to date. If I've missed a new better line for White with 4. Bc4 agains the Schelchter line please some kind soul correct me.

@4
"I feel that your move is the better practical move of the two."
++ Probably: here is a correspondence game with 4 Bc4:

but how would Bc4 be any better other then putting pressure on a Knight that was going to move anyway

Not so much about pinning the knight, but about getting the black pieces out quickly, and letting the Black king castle fast if he wants to. In the normal Morra, Black needs to spend an extra turn moving a pawn before the bishop can get out. Typical Morra setup pictured below, Black to move. Notice no open lines for the Black pieces.

The Smith Morra is kind of hard to play as White anyway. It's a real gambit: you give up a pawn and usually don't get it back. In exchange for your pawn, you get open lines for your pieces, while Black has none. But in a Morra setup against 1 ... e5, you get the position you asked about in your original post. (shown below, Black to move). Now Black has open lines too. What advantage can White claim for having given up a pawn?

It seemed promising to me too, when I first tried it. But when I've played this way, I haven't done well. Instead, after 1. e4 e5, I play the King's Gambit.