They both feature a young woman who is looking for something beyond her home town. In Moonshine, she had left and lived in Tampa for a number of years, becoming a TV weather person. They flipped that to have the character only temporarily leave but kept Tampa.
The "Peanut" character is essentially the same. Some of his "I think . . ." jokes were recycled but not all.
They figured out the guy's con in Act 1 in both versions. "We Love Jesus (but we drink a little)" was in Moonshine, as was a version of "Best Man wins." I'm not sure about the other songs as I no longer have the program from Dallas. They used the same plot line in Act 2 of getting Gordy (whose name was the same) drunk to try and trick him into giving himself up.
In Moonshine, Lulu ran a beauty salon but she was sassy like in the Broadway version, and she and Gordy ended up together as well. I think they signaled the attraction earlier in Shucked than they did in Moonshine and they talked about it so it felt earned, maybe?