As others have said, for most game situations colonies are better. The problem with TPs is that they burn, and AIs always burn them if they capture them. So, if you've put up lots of TPs, and AIs can get at them, you can't really afford wars with them. This is a big handicap inasmuch as warfare is a very profitable way to grow.
But in places where AIs don't know about, or can't get at, I really like TPs. Good places for them are interior North America and Siberia. There are also some interior areas in South America, although fewer of them.
It is true that TPs don't produce as much income as cities do. So in the very long run, you'll want to convert TPs to cities. But they are faster to put up, by far. They only have to average level 3, for you to build another one without penalty, after you've build more than a handful of them at level 1. Whereas, colonies have to average "level 10" -- cities -- for you to be able to build another one without penalty. (Again, after a handful of non-penalized colonies.) So, you can grab 3x as much space if you only do TPs, all other things equal. And of course, building TPs is far cheaper than colonization. So you can afford it even if you're not yet a real superpower. Smaller countries won't even be able to spend all their colonists on TPs unless they use synchronized looting, which is not exactly an obvious thing for a newbie to do.
If you do have money to spend, then the tradeoffs between colonies and TPs are not as clear. For one, colonization chances tend to be higher than TP chances in most of the places you'll want to grab (i.e., sugar islands, any place with high base tax value). And you can use conquistadors to help establish colonies, and both conquistadors and explorers to expand them. Whereas there is no way to get a boost to TP chances, at least, no way early in the game. Later in the game, you get a whopping +50% chance with TPs, so long as you can keep your trading efficiency at 100+. But this is pretty much impossible before about trade 5, and even then you have to get some other bonuses (i.e. go Reformed, build a bunch of refineries, get a bunch of monopolies).
But that said, the return on investment for a TP can be the highest ROI in the game. If you have a CoT only you are trading in, and can plop down a TP on a high-value good, the return on investment can be over 100%.
To take an illustrative case, with 100 trading efficiency and not too many TPs, you get 95% chances almost everywhere. Assuming you've promoted enough officials so that worldwide demand for luxuries is 200%, then many luxuries will have their market price over 2x their base price. The highest value good is almost always fine china, because it's in the lowest supply. Its market price will be around 36d with maximum demand. A new level 1 TP will cost about 15d to establish, and it will produce 1d trade tax, and 18d in trade. So on success you get 127% returns; with 95% success rate this is still a total ROI of 120%. With higher trading efficiency, that rises linearly; I've had TE over 150 in some games.
Nothing else comes remotely close to that level of ROI in EU2. As a point of comparison, the second best investment is colonization of a few easy gold provinces, using a conquistador; I've seen costs as low as 25d to colonize one of the Siberian gold provinces, for an increase in 5d (per year) in gold production. That would be a ROI of 20%. You can also get 20%+ rates by building tax collectors in provinces with very high base tax value (13+).
There's another downside to colonization vs TPing, not yet mentioned. That is that most of your spending goes into tech, and each new city (up to a point) raises tech costs. Since TPs don't result in cities, they do not raise your tech costs, and thus they raise your income without raising costs. Consider a fairly typical 1600ish situation playing Portugal. World trade is at 8000d, and you've gotten 30% of that, with TE 100. So, your net trade income is 200/month. You have 20 cities, i.e. tech cost multiplier of 2.32. Your total province income from these cities and all colonies and TPs is 50/month. You can build new cities producing 3d/month each (about what you'd get from a sugar island). Any new city or a level 6 TP will raise your trade in Tago slightly (20d/year, but you only capture 6d from that). The level 6 TP would generate about 0.5d/month in trade taxes. Adding a level 6 TP thus increases your income by 1d/month, without affecting tech costs. The effective rate of tech investment is proportionate to your TCM divided by income; in this case it improves from 2.32/250, to 2.32/251. Adding a new city with 1000 pop increases both income and the TCM. So the new rate would be 2.345/253.5 . If you work out the arithmetic, you'll find the tech rate is increased faster with the TP than the colony. (And of course, it would really be fairer to compare 1.66 TPs vs one colony.) Thus, for hyperteching with relatively small countries, TPs may be superior to colonies.
One more good point was raised by Misconstruction, above. Unlike cities, TPs do not raise the supply of their good. This does not matter for most goods, because either they are in massive supply anyway and will never be high price, or else, the total number of provinces worldwide which make them is not that high. (I.e., there are only a total 30 provinces which make fine china, so supply of it can never exceed 80.) However there is one luxury good that is initially in low supply, but which has zillions of provinces which can eventually swamp the supply. That good is furs. (Initially there are just 27 cities producing furs, and a few colonies in Europe; but worldwide there are 102 provinces with furs, so that total supply can be maxxed out at 150.) This oversupply point is another reason why Siberia and North America are a good places for TPs.
