Build-wise, the burgers are identical except that the Hardee's version comes with a sesame seed bun, while the Carl's Jr. one comes with a plain bun.
First up, the Carl's Jr. photo:
You can see creases in the bun and it doesn't have an abnormally perfect rounding to the shape. Likewise, the cheese is creased slightly at places. The tomato has a slightly under-ripened tone to it. There are just a few bits of onion peeking out from beneath the top bun.
The beef is charred but the grilled marks aren't as prominent. Finally, these's a little crumb next to the bun to suggest, "Hey, a human made this."
Now, the Hardee's photo:
Everything is a little too shiny. The meat is glistening with char marks that somehow reach down the sides of each patty.
The tomatoes are a too-perfect bright red and the bun is a little too buoyant. The sauce looks like it was artfully decorated onto the burger and the onions seem like they were all pushed onto the front side to be seen. The result makes it look like the burger fillings have been almost superimposed on the bun.
It's a bit puzzling that the sister chains' decided to go with different pictures for the same burger but gives the juxtaposition gives an interesting look at how burgers are marketed. Personally, I prefer the Carl's Jr. photo but maybe customers are more likely to buy the burger looking at the Hardee's one?
McDonald's actually put out a video of how they photograph the too-perfect burgers in their advertisements a while back. It's an interesting behind-the-scenes look at food photography that you can find here.
In case you're wondering, my photo of the actual burger when I reviewed it turned out like this.
Photos via Carl's Jr. and Hardee's.