Yes. It's my main issue with the game on deity and have been for some time, the massive bonus shower the AI get -- you can so clearly see if when the bonus overflow kicks in and a city just produces two-three units in a single turn or how they in a span of a few turns just crank out multiple technologies or as soon as a city goes down the wonders starts being built, not to mention when they switch era.
Sure you can keep up for a little while in the beginning but at soon as the AI starts to plop down their second and third city or so they'll just explode in power and before long they'll be 10-15 techs ahead of you and have an army that will far exceed your cap and all you can really do is just bite down on the giant s**t sandwich and wait for the some runaway AI to get far enough ahead so you'll get some spies and can slowly start to catch up again -- usually in late renaissance and industrial era, but it depends on the settings, geography, your neighbors etc. But by then it's usually to late cause some snowballer on the other side of the world has now built all the wonders and are just crushing all his neighbors left, right and center.
While being 10+ techs behind is bad, it's not the worst part of it. The worst of it is usually how being so far behind in quiet a short time just makes your stability/happiness crash, unless you prepare for it and it's not always an option, which makes catching up even harder.
There is no "play good" to be able to catch up or hold parity at this stage of the game. There has been various shenanigans you could engage in the try and keep the AI at bay, some might even call them cheating or creative bug usage but you can't compete on normal building with someone that just gets hundreds of free bonus units (prod, cult, gold, food etc) for nothing.
It's not really that civ-specific I found but it can just happen with any ai-civ, it's just seems more common with some of them since their bonuses help a little but it's quite small compared to the bonuses they get so it's almost irrelevant whatever civ-specific bonuses they get. At least that is my experience.
I guess the late few patches, sept and oct, made it a lot easier to get a religion again on deity. Somewhat related to the AI not getting the bonus on capital foundation, but the bonus shower just moved a bit further down the line I gather. So you'll have a fairly nice start most of the time -- you can without issue get pyramids/stonehenge if you like etc to but after that it just time to hunker down. Fighting into someone that is 10+ techs ahead of you just plain out sucks.It also seemed to be related to how the AI see you and when you are that far behind they'll just start chaining war declarations against you even if they are on the other side of the world and you'll never even see each other on the battlefield.