What whites gains is:
The open c-file.
2 center pawns vs. 1
Pressure against c7.
After Qb3 pressure against the bishop, d5, and b7.
What whites gains is:
The open c-file.
2 center pawns vs. 1
Pressure against c7.
After Qb3 pressure against the bishop, d5, and b7.
What whites gains is:
The open c-file.
2 center pawns vs. 1
Pressure against c7.
After Qb3 pressure against the bishop, d5, and b7.
But now this image.

This is in the Fritz (14) book. Also whithout the book Stockfish favors Rc1.
Why isn't cd: not right in this occasion, as it it would meet all of your mentioned advantages.
What is the essential difference?
First of all. I need to know what you mean by "favors" If you are asking why an engine prefers one move over another by something ridiculous like .10???? There is essentially no difference.
Besides all that. You're asking about 2 different positions.
But in the second position. 1.cd5 doesn't work due to the following 1...Nd5 2.Nd5 Qd5 and black has a HUGE lead in development. And if 1.cd5 Nd5 2.Bg3 h5 black has pretty much everything pointing at the kingside.
Thank you IMBacon & inkspirit!
The context is that I've engaged in a little project to discover the motivations for c4xd5: in the Queens-Pawn (and later QGD) openings beyond the trivial tactical motifs. By extension, I'll also check out d5xc4: from blacks perspective, again beyond the usual tactical motifs.
White played 5. cd5:
See screenshot.
What does white gain from this move? In many cases white doesn't break up the center with cd5: for quite a while. So, in this case, what does white achieve (or prevent) with this move? How is it better than, say, 5. e3 or 5. Nf6? (says a recent Stockfish engine).