The thing with Ideologies is that they favor certain conditions within your empire.
Autocracy is for those who find themselves behind the world with little room to catch up peacefully. This is what you take when you're only now getting your Factories up when both your neighbors hit the Atomic. It's not good when you're strong and in the lead with things, because you'll have little use for that obscene happiness or super tech stealing, but when you're in a potentially critical position where you're likely to lose, this is what you get. It is very very very much a "turn the tables" ideology in that respect.
Order is probably the most solid of the ideologies, simple and effective but not outstanding in its benefits. It gives the best bonuses for kind of naturally flowing into higher production and science and growth and other things, and is easily the most attractive for those with mid-sized empires. Where it REALLY shines is if you have a situation with a potential new frontier, the likes of a Terra map or one with otherwise lots of space that can still be settled, because that territory can quickly turn into a race once conditions collapse and you have so much money that you can afford to expand, and need to expand fast...but in the bog-standard-condition map, that is not going to be the case, as borders will be functionally cemented by the Industrial era. All in all, it's the most balanced of the ideologies, I find, what you pick if you're going strong and want to keep it that way, and its biggest tide-turning advantage can be lucrative, but on most maps, not used that much.
Freedom I find is a bit hard to encompass. I feel like I want to say it's the flip side of the Autocracy coin, but in a sense it isn't. Basically put, with Freedom, you're gunning to slash your way into a victory in the most precarious but potentially devastating way possible. Autocracy is gambling to stay afloat and compete in the late-game to get the kind of big empire for later prosperity - Freedom is skipping that step and getting to the victory right then and there in the shortest amount of time possible. Out of all the ideologies, it's the hardest to defend with, but if you can defend yourself, you're likely to come out on top. Very much a "sniper" ideology, where you can suddenly nab power from thin air, and gun for any victory really, you just have to do it FAST. You can easily axe ludicrous amounts of Culture and Tourism, you can get spaceship parts in one fell swoop, you can amass a World Leader vote with incredible speed, and hell, you can even go capital sniping effectively, but you can waste no time whatsoever. In more moderate senses, it is particularly excellent with maintaining a specialist population, and rewards you for going crazy tall. It's riskier than Order because it offers less up-front production and Science, but allows you to generate even more if you're smart enough about that. In a sense, it's peacefully reckless, where you're scrambling to get all your yields amped up as high as you can, but rewards you greatly should you manage to do that.
