Yeah, it's similar but Archive.org relies on servers to store information, whereas Arweave is a decentralised peer-to-peer network that offers permanent data storage. Arweave are in talks with them and are working with the IA to timestamp all of their collections.
Definitely. OnionShare requires your own computer to be connected to the interwebs - the data is only accessible while your OnionShare app is running. With Arweave the hosting is taken care of (the data/website/etc is hosted on the Weave). Plus, OnionShare sites are not verifiable/ reliable as they are a website running on someone's computer. An Arweave site is timestamped and unforgeable; it's also resilient (replicated on many nodes) and permanently stored.