FWIW DRS is based on people watching film (the same as PFF grades in football) while Statcast is based entirely on data using the hawkeye cameras tracking every game.
Everyone's mileage will vary, but I tend to split the difference between the two with infielders, while on the outfield I trust statcast pretty implicitly. There's a ton of relevant context on a ground ball: speed of the runner, quality of the hop, minor changes in positioning affecting what direction you approach the ball from, other baserunners, etc. But on a fly ball? Short of inclement weather how far you had to go, in what direction, and how long you took feels like it covers it pretty thoroughly.
I tend to think this team is fairly incredible up the middle while on the corners it's fairly average, maybe a smidge above. Shaw's got enough speed I could see him juicing the corner outfield spots pretty significantly, and definitely already does 3B.