As I mentioned in that other thread on Liberty, I'm playing this game a third time after reading some of the Liberty strategy guides. I didn't change all that much from my first time (and I've scouted the map the same way all 3 times to try to not take advantage of prior knowledge.)
I settled the same 4 cities but one of them is on a different tile, and my pantheon and build orders and ancient-era tech order were different. I may still settle 2 more cities but I think I want to get a few more national wonders first (especially Heroic Epic, Ironworks, and Grand Temple.) I have puppeted an AI capital and another city, and people still want DoF's and research agreements with me.
Small differences in the early game can be huge 100 turns later. I think I was trying to play Liberty like it was Tradition.