|The manga is a super summary of the anime like the others have said. However, the anime is alot better and the soundtracks to the anime are some of the best.
Spoiler (highlight to view)
In the manga after Eureka becomes covered in the Skurve, Renton works on repairing and upgrading the Nirvash type zero. In the Anime a new arc begins that is left out of the manga where Renton leaves the Gekko-Go and meets somebody called Charles and ends up flying with him and his wife. Eventually, Holand kills Charles and Renton retuns to the Gekko-Go. That's just a super short summary leaving out many details but the whole arc takes up about one season of the anime so I would recomend alteast watching that season so you can see for yourself how different the manga and anime are.