Shangri-La

Both series are based on different novels that use a similar post-apocalyptic setting where a community of people forgotten by society lives outside a fortified utopia. 

I can't really put my finger on it but there's something that reminds me of Shangri-La. It has been lingering in my mind since I started the series. If I tried to narrow it down to something, I would say it's the overall feel to both series. Also the content of the stories are quite similar. Young protagonist/s trying to find the truth about their twisted society. Both are entertaining and take suprising twists. I recommend to watch Shangri-La if you liked Shinsekai yori and vice versa :) 

World in the future, new technologies and organization fighting for freedom. Both have some similar supporting characters. 

Both are centered around a young girl who seems on a higher level than the people around her, peace-loving but an adept fighter. They also both take place in a grim future where mankind's abuse of the environment has created a toxic, jungle-infested planet that is difficult to survive in. 

Other than energetic main characters, both anime seem to present a futuristic world divided between castes and the world ruled by a particular resource. For Last Exile, it's airship technology, whereas for Shangri-la, it's carbon. However, Shangri-la is set in the near future and has a strong environmentalism and corporate power issue brought up. 

Apocalyptic future, boy & girl involved with great rebellion and conspiracy fighting against government.  

Both shows revolve around 18-year-old girls with superhuman strength who help people in a post-apocalyptic Japan, caused by a disaster that occurred some time before the story started- in "Shangri-La", the disaster was an earthquake, while in "Coppelion", it was a nuclear meltdown. In both cases, the main characters belong to a group that regularly looks for various essential items in order to survive, though "Shangri-La" eventually evolves into more than just a fight for survival. Imo, neither show is particularly great, but I'd say if you like one, you will probably like the other.  

Shangri-La and Black Bullet both take place around Tokyo after some apocalypse has occurred. In Black Bullet, the main characters fight for the safety of the survivors; while in Shangri-La, the main characters fight for better living circumstances for the people. But most importantly, both anime have badass lolis. The main differences is that Black Bullet is mostly action while Shangri-La also contains economics and environmentalism.  

In the distant future; where mankind suffer to live through a bad earth condition, forcing themselves to live in a strictly controlled society. Both series feature a strong/skilled female protagonist who's trying to figure out the mystery behind what's called "The Perfect City". Both series contain a decent level of bloody action with superb art quality. Ergo Proxy does obviously have darker atmoshere, while Shangri-La is a bit more lighthearted; but still has its own tragic moments. Although having similar story concept; they actually deal with different themes; Ergo Proxy: Psychology, Cyberpunk, Hardship, Amnesia... Shangri-La: Economy, Politics, Leadership, Hacking, Prison... 

basically roppongi and a gay bar. finished grapher before this and felt like these two were connected in the same universe  

The city of setting are both destroyed by a massive earthquake and everything and everywhere are wrecked. 

Both are tales of two younger individuals coming into their position and finding out what their ideals are, and fighting for those ideals. Both have some level of economy, and politics, and both have some level of high society. 

They share a similar setting - dystopian future, uprising against the dictatorial regime, people outside the secure/rich zone trying to get in - as well as some plot points. Shangri-La is somewhat better. 

Both contains morall choices, supported by friends but in the end the heroine fights on her own to save the world (Ringo in MP and Kuniko in S-L). Sad, but somehow filled with hope. 

The same studio producers. Both have a very similar visual designs and both plot-lines also have an element of nature having taken over. 

Supernatural + earth ecology + a spot of romance are to be found in both 

Similar type of sci-fi with focus on environmental problems! The artstyle is similar, though I prefer Shangri-La's style more than Terra e...  

Futuristic shows where the main character is the head of the rebellion of the weak against the dictatorial rule of the high-class people. The plot is intricate and complex, and the shows share the same genres. 

The theme of science fiction is present throughout both series as we can see that the planet/world that the characters resides in have different policies and structures than our own. Shangri-La and Suisei no Gargantia both takes place in the distant future. Among the settings, humanity lives on their perspective planets but faces struggles. There are also secrets behind the backgrounds related to some of the origins of the series. The main character from both series also has possesses military intellect and skills along with an unique weapon/partner. Among other factors, both series has an utopian like background that gives off a similar vibe.