Shortstop
So far, the Cardinals have a 3-0 lead in the position battles, but this is where things get interesting for the Brewers.
Willy Adames posted a 120 wRC+ in 2021 and looked like a force at the plate for Milwaukee. He hit some regression in 2022, dropping down to a 109 wRC+ but still boasting a ton of power with his 31 HR. Many will say that Adames is a superior hitter to Tommy Edman, but in 2022, Edman's wRC+ was 108, just a tick behind that of Adames.
I would expect Adames to bounce back some in 2023 and outproduce Edman at the plate, but I don't think it will be a large difference. They are two different kinds of hitters. Adames is more of the big power bat that doesn't get on base a ton but does damage, while Tommy has a much higher OBP and is a doubles machine.
Where there is a major difference in performance for the two is their defensive ability. In about half as many innings as Adames had at shortstop in 2022, Edman had more outs above average and fielding runs prevented while having just 3 fewer defensive runs saved. Adames is a really good defender at shortstop which oftentimes goes overlooked, but Edman has shown he is clearly better, especially if he is given a full season at the position.
So, based on 2022, I would say Edman is the superior player here. For 2023, it could really go either way, but I'll go with the guy who finished 13th in all of baseball in WAR (Edman) over Adames coming off of a down year.
Advantage Cardinals, but not by much.
Third Base
This is basically the same story as first base. The clear advantage here is for the Cardinals, and it's probably an even wider gap here.
The same options the Brewers will be relying on for second base (Toro, Miller, Urias, and Turang) also happen to be their third base options, and they are league-average players at best.
Nolan Arenado is coming off a top 3 MVP finish in 2022, another Gold and Platinum glove, and is my early pick to win MVP in 2023. His 130 wRC+ mixed with elite defense makes him one of the best players in baseball.
One again, advantage for the Cardinals.