I'm playing a Terra Map right now (Napolean, Standard, Noble). In fact, I think Terra maps are my most favorite type of map.
In my current game, I was started in a moderate location in the northwest corner of the Old World, where I was able to found 5 cities. Hatshepsut had me boxed in to the northeast while Saladin had me boxed in from the southeast. Even though I had Open Borders with both of them, I decided not to escort a settler through their lands to grab any property on the other side. Instead, I just chose to build up my infrastructure.
My general plan was to make a moderate push to get Musketeers, and to try to also found a religion in the process. Ended up I was able to found Confucianism, and spread it to every Egyptian and Arabian city. Saladin converted, but Hat just kept getting madder. At about the same time as my caravels were making it to the New World, I was discovering Gunpowder, and Saladin was declaring war on Hatty (I had nothing to do with it).
So I decided to prepare a colonization attempt instead of heading off to war initially. I figured that Saladin would come ask me for help in a few turns. I ended up getting my first colony established in the new world before Saladin asked me to assist in his war so I decided to declare war independently.
My musketeers were able to quickly dispatch of three four Egyptian cities, razing one, and capturing the other three before Tokugawa (who also had declared on Hatty) finally wiped her out. By this time, I was up and running with five cities in the northern half of the New World. Two were captured from the barbarians, while the other three were self founded. Some early wonders produced a great engineer, and by the time I retired for bed around 4am, my centermost New World city contained the Versailles wonder.
Peter seemed to get mad when I used a great artist to expand the borders of one of my New World cities and ended up enveloping his initial colony. He declared war on me, and we are entrenched in a tough border fight in the Old World. He is coming at me mostly with Grenadiers and Rifleman, and I am defending with the same. I am hoping my recent discovery of Assembly Line and infantry will swing the tide of war in my favor.
Also, there are two remaining barb cities in the New World, and once I get a few infantry and cannon over there, I'm hoping to capture them as well.
This is radically different from my last Terra game in which the most anyone was able to establish was a single colony in the New World. The New World was ruled by barbarians, and the Old World was plaqued by constant warfare. I was the Aztecs, so I didn't mind. I ended up winning a time victory.
Essentially, I think both of the aforementioned strategies can be good. In my French game I think I will most likely try to go for a diplomatic victory. With my New World holdings, I should have enough land to project my power of that continent, and grow my empire to where I have enough votes to win. In my Aztec game, I was trying to obtain a conquest victory, but was unable to eliminate the Germans and Rome before time expired.
Glean from it what you will, but that has led me to formulate two basic strategies for Terra Map play.
1. Build a solid core of 4-7 cities in the Old World, solidify your military strength, get to Astronomy quickly, and expand rapidly to the New World, or
2. War early and often in the Old World, stunt your opponents' growth, and never allow the New World to develop.
I always play Civ4 trying to capitalize on my Leader's traits, and I've found that Terra maps can really accentuate the differences between the civs.
Just my take.
MM