I haven't noticed any particular pitch-calling advantage for Gattis. Examples?
IIRC, last night, first batter, lefty, 2-1 count. Musgrove on the mound, who normally competes with his FB command and his slider. I'm expecting a FB to get back in the count, maybe the slider if they want to go backwards. Instead, Gattis calls a change, which for Musgrove is a pitch he can command, but is easily inferior to his other offerings and is pretty squarable in a lot of situations. The hitter makes solid contact, but is off balance and flies to center.
Later in the first inning, he called the change against a righty, which IMO, is unexpected by Musgrove first time through the order to a righty. The hitter was also off-balance and fouled it, IIRC. The long bat to Vogt seemed to feature a lot of pitches I did not expect.
In general, Gattis seems unafraid to call pitches multiple times in a row. There have been a number of times with McHugh where he will call the hook many times in succession to a hitter who looks have trouble with it. Rarely does Castro go to it more than twice in a row.
IMO, Gattis calls a game like a hitter who is thinking "what pitch would I either not want to see at this moment, or not expect" whereas Castro is more conventional, based on the pitcher's strengths. In other words, I am not often surprised by a pitch Castro calls (he calls like most catchers I see), but am often surprised by what Gattis calls.