Shortstop is one of those positions where if the offense is reasonably close, I always go with the better defensive player. Since I don't expect much more from Cozart, I think ultimately he and Gregorious will be reasonably comparable offensively. Since Gregorious is the better defender, I would go with Gregorious.
Throw in the age difference and I actually think it's pretty clear cut.
The one thing this doesn't consider is trade value. I'm guessing Gregorious probably has slightly higher value, but since I doubt it's significantly different, I wouldn't let that impact the decision.