Plaza premium is convenient for me when I've been to DFW as I fly F9 and it flies into the gates where Plaza Premium and one of the game lounges are in. I have to take the tram thing to go to The Club. I have taken the rental shuttle directly to the Terminal where The Club. The TSA line has been longer there vs the Plaza Premium terminal.
I liked the food at Plaza Premium better. It has had a solid protein option for me: meatballs several times and chicken satay sticks two other times. I like the drinks better at The Club. Plaza was limited in free alcohol options.
The Club is better for lounging around waiting for your flight as there's more room. Plaza Premium is a really small space. I get my food and then get out of there. I'll head to the Club if I still have more time to kill but usually I'll just hit the Game way lounge or whatever it's called. (CSR PP still offers this along with the massage chair place).