Not correct.
100 tourism + 100% bonus = 200 tourism (Order)
133 tourism + 66% bonus = 220 tourism (Freedom)
All other things being equal, the city bonuses is superior.
All right, I concede that Freedom may be better at influencing OTHER ideologies in a straight fight. However, Order is still better at influencing the same ideology:
100 tourism + 143% bonus = 243 (Order)
133 tourism + 75% bonus = 232 (Freedom)
Without DotP, Freedom does pull ahead (Order drops to 209), but remember what the original statement was:
Freedom's culture T3 is arguably the weakest, because even though it is the most versatile, Freedom has no big "everything" modifier to really slam it out against differing ideologies. Order's Culture T3 is potentially the strongest, but only on a narrow band.
On that narrow band, Order is superior.
Now, that said, it's obvious that which is actually better is going to depend on the target civilization. If you're going for a Tourism win, your choice basically depends on the other civilizations - it doesn't even matter what the trees are. If the biggest culture is on a Freedom civ, you need to go Freedom. If it's on an Order civ, you need to go Order.
The +tourism bonuses in the actual ideology trees are irrelevant. What matters is what the other civs are.
Not necessarily. If you're going for culture win, you will likely have the luxury of picking the ideology that everyone follows, so you can pick based on whether you're tall or wide or if you want to win by Diplo, rather than what the big guy goes for. The big guy may just have to be annihilated one way or another -- what matters more is not what he picks, but what the rest of the world picks, and on that front, the AI -loves- Order.
However, the debate over Order vs. Freedom is more a debate of Tall vs. Wide. Nobody picks ideologies in a vacuum. If you're tall-with-Tradition, obviously you want to pick Freedom, and if you're wide-with-Liberty, you want Order.
I was responding to a specific claim about comparing specifically the tier 3 tenets of Order and Freedom. If you want to talk about something other than the tier 3 tenets that's a different topic.
We cannot take the tier 3 tenets in a vacuum just because it's convenient for your argument. None of the ideologies were designed in a vacuum, and as such, none of the tier 3 tenets were, either. Freedom may be able to purchase the spaceship parts once it reaches the very end, but that makes Space Procurements *completely useless* until the Information Era, while Spaceflight Pioneers grants 10 base science in the capital, making it more useful the earlier you take it, and it is available right around the early Modern era. If 10 base science in the capital were useless, nobody would build research labs. It adds up.
Freedom does have the edge if it reaches the end first, but as with the World Games Win, Order is simply better equipped TO reach the end first, regardless of tier 3 tenets. If we really must compare a Tier 3 tenets in a vacuum, however, then Spaceflight Pioneers is clearly superior, because it actually *does* something before the information era, and even still allows rushing of parts, even if it does require something more than gold.
On courthouses versus city-state influence: Of course they are 100% comparable. Don't be ridiculous.
Rushing a Courthouse costs X gold, and the tier 3 tenet automatically does that for you. It's worth X gold times the number of cities you capture, though admittedly there are weird little scenarios where you get a small temporary happiness boost while raising a city.
Buying city-state influence costs Y gold per influence. The tier 3 tenet provides Z influence per turn. It's worth Z*Y gold. It all comes back to gold.
If you must compare gold to gold, then Iron Curtain is
vastly superior, because it can be used for every city in an opponent's empire, in rapid succession, multiple times per turn, and can be used on cities you have no intention of keeping while you destroy them, which is otherwise IMPOSSIBLE with gold alone. That scenario is anything but a weird exception -- if you're going for domination, you're not keeping every city you conquer, you're razing the vast majority of them. It easily saves you thousands, maybe even tens of thousands, over the course of a Domination game, especially if you obliterate wide empires, the likes of which are usually runaways that need to be stopped anyway. Treaty Organization, on the other hand, takes a long time to do the same job as a pure gold infusion would, and in the meantime, you're using inferior City-State trade routes instead of capital city trade routes, which severely blunts the gold savings you'd get from it.
If you want to compare them gold-to-gold, then Treaty Organization gets utterly thrashed by comparison. I'd argue that even Arsenal of Democracy is superior to Treaty Organization on the same metrics, because it turns 125% of your production into gold without costing you an actual penny. It's a good thing, then, that TO and IC are for
totally different things and don't compare to each other
at all. Why you would adamantly pick such a battle is beyond my comprehension.
with WC policy... 
