I never played Tropico 1 or 2, but I do enjoy Evil Genius, Dungeon Keeper and Dwarf Fortress. I love games that let me build up an empire and repel attacks without being completely focused on combat all the time as in a standard RTS.
This game has a lot going for it. Think "Sim City" with the additional need to balance out political factions and put up with rebels. In Sim City, unhappy sims would simply leave. In Tropico 3, they're more likely to pick up a gun and try to overthrow you directly.
That said, the game has some faults that are making it into a pretty short lived affair. I've put in maybe 8 full sandbox rounds and I don't think I've got many more left in me.
The problems I had:
* It's too easy. It's not hard to go through the whole game without a single rebel. Factions are easily made happy and the extreme measures of dealing with rowdy individuals available to a tropical dictator seem to be unnecessary. Even if I configure a custom game with politics as unstable as it will let me and with "Rebel Yell" turned on, which makes my citizens even more likely to rebel, I still find rebellions aren't that big of a threat. They're even less of a threat than the occasional invading party in Dungeon Keeper.
* Combat is too forgiving. You don't really have any control during combat, which is fine, really, but the mechanics of it are still rather silly. When the rebels do finally show up, they will try to sabotage a structure and run away -- except before they do this, they will politely stand near it until literally your entire army has shown up. Consequently there's no reason to plan out how to distribute your guard towers to deal with threats quickly. Just build all your military stuff in one place and put a parking garage nearby. The rebels will wait until you show up, no matter how long it takes to get there.
* No "win" condition + no persistent scoreboard for the sandbox missions. Although the campaign has victory conditions, in "sandbox mode", which lets you play a randomly generated island, there's no victory condition. You rule for a set period of time and then the scoreboard comes up. The only measure of whether you did well or not is your score, and it doesn't save your score, so you have nothing to compare it too short of writing down your previous scores. So I love that there's an ability to play randomly generated maps (something I wish more games would do) but I think it could be implemented better.
* The foreign invasion is literally just a "game over" mechanism. I once played the game aiming to annoy the US because I wanted to see what it was like when the US invaded. Could I make a big enough military and fight them off? No. The scoreboard just pops up. You lose immediately. Rather anti-climatic.
But it's not all bad news.
The game is beautiful. 3-D, high degree of zoom-in and zoom-out, individually modeled citizens are roaming around and clicking on them shows you all sorts of useful information: what does this citizen think about their job, their health, crime, freedom, etc? What's really annoying them? What are their thoughts? (Thoughts are a good quick way to see if people are missing something in particular, e.g., "I wanted to go to church but couldn't" -- you may not have a church or you may need another one or you may just need more priests for the churches you already have.) The level of detail involved in managing your workers keeps you busy too. Tropico is not an equal opportunity employer. Some jobs only take men. Some only take women. Some take both. Sometimes you have to fire the men working on the farm to make room for unemployed women while the man go off to fill out the lumber camp. You have to deal with education because some jobs require high school or college to work there.
So there's plenty to play with in just running your town.
Basically I think this is a fantastic "sim tropical island" and if you want it for that, well, look no further. If you enjoy Sim City type games you'll definitely enjoy this. I was mainly disappointed over the lack of depth to the combat. Not that I was expecting a full on RTS but I definitely expected more than the rather weak and unstrategic rebel elements the game has.
I'm still holding out hope that they might change how combat and politics works with a patch. There needs to be more room to up the difficulty. It could be a great game with just a few minor adjustments.
As it stands, I rate it 4 stars for fun, because it is fun, but 3 stars overall because it just isn't something I got a lot of longevity out of.