Going for UN victory: Freedom clearly superior. (Nothing from Order, but Freedom has a level 3 tenent that will give +4 influence per turn in city states in which you have a trade route.) Autocracy also has gunboat diplomancy, but you need a large army and troops throughout the map to get this so it's much harder to use.
Culture victory. All have some bonuses, an above poster has mentioned Order's biggest one.. But I think provided you secure CN Tower (alternative build Broadcast Tower in cities in which there is significant tourism), then Freedom will be superior with a 34% boost; again a level 3 tenet. Also there's tenents within freedom that for all specalists, including guild ones will increase growth & happiness. Autocracy's culture bonuses appear underwhelming by comparison.
Spacerace: I think Freedom is superior; even if you can faith buy GEs. Getting the gold to cash rush space race parts is much easier. In my previous game, I cash rushed all but one part.
Domination: Order is clearly better than Freedom here. But I think Autocracy is even better for domination. I guess the main question is why isn't the game already effectively over going for Domination by the time you can choose an ideology given that the earliest you can reach it is Industrial era.
Freedom & Order both have some indirect bonuses that apply to all victory types.
Freedom's is focused on specialist use and working great tiles. This basically allows Freedom faster growth and a massive happiness bonus from those specialists. Combine with Rationalism & Statue of Liberty and you can get quite a boost by running all specialist slots. In addition those Academies you built will now produce more science / landmarks more culture etc.
Order is much more focused on buildings, especially the factory. (If you've not yet built all factories, a big boost building them; a science boost in all cities with a factory) And 10 science in your capital helps for all victory types even if its not as much as a single Freedom academy.