Before emphasizing the differences, we'll start with some features that are similar in each of the decks. The first common feature is that all decks are printed in chromolithography.

The second one is the shadow -as a tromp l'oeil- of the circles and cards to pretend that they are detached from the image.
The third common feature is the double outline around the complete image, although not around the (playing) cards on Carreras # 2 and 3. And, last but not least, the same type-font was used for the numbers.

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But of course there are differences too. These differences are caused by the fact that the Carreras cards have a different size than the original Dondorf cards. To print the Carreras cards in lithography a new set of stones had to be made and this means that the scene had to be redrawn to fit the size. 

Because the almost square Carreras cards don't have the height of the original, the design had to shrink.
An obvious choice was to reduce the height of the playing card by a few mm, but it was inevitable here to shrink the height of the scene as well.
Of course it was also easy to reduce the quantity of air and cut down a bit on the bottom, but for the shown Carreras card #1 this has also led here to shorter legs on the horse and even the rider seems to have a shorter torso and his position is a bit less up-right than on the original card.
As the Carreras cards #1 are also wider than the original, a part of the landscape was added on the right.

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Dondorf #3

Carreras #1

On Carreras #2 and 3 that same part was left out again, but as the cards are relatively higher and narrower than the Dondorf cards, more air and soil were added. Another consequence is that the playing card is higher up in the complete design and has only one outline now. However, the design of the horse and rider, the house, trees and landscape are exactly the same as on Carreras #1.
There is a difference between Carreras #2 and 3 too. The colors yellow and dark green, that were applied on Carreras #2 (and #1) were left out on Carreras #3. 

As the basic design is apparently the same, the backs here below are shown at different percentages for comparison of the effects of the different sizes on that design. But apart from the widening and narrowing, some other differences can be seen. The B.D. initials have been deleted and advertising text along the sides was added. The color dark pink was left out and more blue was added. The circles in the middle have a dotted pattern and the outline, making the rounded corners, was hatched, making it look more like a rope.

Dondorf backs #3 and 4 are shown at ca 60%, Carreras back #1 at ca. 75 % and Carreras #2 at ca. 85%.

Carreras #2

And.... for some reason only on Carreras #3 four curling branches with leaves were added.

Carreras #3