Zync has a lower annual fee and you can add "packs" for a added annual fee to get double points in certain catergorys. The fee is not waived for the first year though like the green. I have both and I prefer the zync.
Some key elements to consider for both cards is the annual fee, and the rewards programs. Do your research and decide which works for your situation, because at the end of the day it really comes down to YOU. I am a current green card holder, and I am going to ask Amex to change my account to Zync in February. The sole reason for me is the annual fee. $95.00 AF for the green card is too steep for me. I am going to compromise on the color, because I dislike the color of the Zync.
It's all based on your spending and what will benefit you the most. Zync & Green has different rewards and other options.