Normally i would say 1v1 is harder on the high levels because you make x-fers. On Sid, the 1 AI will simply outresearch you. Therefore, you would need to win early with AA units. It might be possible and maybe even relatively easy to win this if you are on the same continet, start with bronze working, do a min run on Iron working and a massive warrior upgrade. Only your best few cities need to be making warriors then. All other cities could be making catapults possibly by pop rushing even.
This requires a good distance on one continent, a distance where you do have the ability to expand to 8 cities or so but close enough that you can attack his core with your swords/catapults. Also does it require iron.
If not these conditions, i think it will be harder than normal sid, maybe impossible. Therfore i go with the deity option. Deity AI's can be outresearched and outproduced.
On levels lower than deity, i think 1v1 makes the game easier as there you are not getting much trade deals from the AI and generaly are the tech leader.