I had serious reservations about this game, believing that this would be a huge step down from the PC version --- a fair concern given that these games, almost always, are massive letdowns after stellar PC versions. Somehow, Kalypso avoided this issue and made a really good strategy/simulation.
You, of course, are a Latin "leader" of assorted island nations. All have issues that you have to overcome, such as poor land, rebel discontent, and the US and USSR not being fond of some of your decisions. That the deep strategy (far deeper than one would expect) has impressive humor and biting sarcasm combined with it makes the package all the more appealing.
You can cheat in the game if you wish...but it does away with achievements, so it is pointless.
You can choose what kind of economy you want to have. You can stick with farms or move into higher levels of industry. Strategy is a bit of a challenge as it is difficult to really plan far in advance as you are frequently struggling to make ends meet at that moment in time. This is a key part of the challenge, as you have to correct earlier mistakes to allow you to develop more completely.
Having to juggle numerous different things (my favorite was to be officially pro-USSR while having an alliance with the US, which seemed to satisfy both groups and kept me popular with both capitalists AND communists) is always a challenge and normally I flounder at these affairs, but this game made everything make some sense. That you being corrupt is almost expected is even more amusing.
Tropico 3 is the best sim/strategy game on the 360, surpassing Civ Revolution. A game so playable and worth your time that little outside of Tropico 4 really is able to compare.