Start at address so you can ensure that you have a flatstick that fits your body and posture. Unlike full-swing clubs that droop and bend significantly in a dynamic motion putters stay about the same during the stroke so getting a length and loft that complement your setup is an important first step.
The Z 585 is slightly more forgiving and features a high-strength steel face insert in the forged clubhead for higher COR and ballspeed at impact. A new internal “speed groove” behind the clubface further enhances face flex across a larger area of the hitting zone for extra forgiveness on off-center hits.
Putters with more forgiveness and stability like larger mallets typically provide superior distance control because they maintain consistent ball speed and roll even on mis-hits. Unless you’re exceptionally accurate with your contact point (repeatable impact in the center of the putterface) don’t fall overly in love with the more traditional head shapes.
Check them out and see if one is right for you but keep in mind the TS2 is aimed at those who want high launch low spin distance and forgiveness while the TS3 is aimed at those who want mid launch low spin and enhanced workability.
There are differences however including most notably more adjustability in the form of Titleist’s SureFit CG technology that allows for more specific spin rate and launch angle tuning. The TS3 also features a more traditional pear shape and tends to produce more of a mid-launch as compared to the TS2’s higher launch.