They dont let sites opt-out, and they do a much more seamless job of enabling people to archive paywalled content

You can access pages that are still actively behind any given site's paywall.

Wayback Machine lets you select snapshots in a calendar without thumbnails, which is better for navigating among a large number of snapshots, while Archive.today shows a chronological dump of thumbnails, which is better for noticing visible changes.

Archive.today is better at getting through paywalls, the Wayback Machine doesn't really do this.

And while not a functional difference, but imho quite important: The Wayback Machine is ran by a 100+ employee non-profit registered in the USA, which lends it quite a bit of legal and financial stability, but also subjects it to official oversight/censorship, while Archive.today is ran by a single mysterious dude who carefully hides his identity, and we don't know where the most of the site's finances come from. (Edit: In one of the posts copied below he mentioned that he has some donations and ad revenue, but as of 2021 this covered less than 1/3 of the running costs.)

Both financial security and resistance to censorship can be useful attributes to an online archive, but I have more trust in the Wayback Machine being online in 10 or 20 years, than Archive.today.

Edit The archive.today owner has a few blog posts mentioning these kind of things:

July 27, 2021:

anonymous:
Not respecting people's privacy, copyright laws, or the veracity of content on your website... Please tell us more about how this archive isn't being well managed and is doomed to die at any moment!

archive-is:
Of course, it is doomed to die at any moment (you should not have any illusions, as well as about the “veracity of content” on the Internet). The only idea is to hold back a little something that is doomed to die a little earlier. I hope that it is obvious after all the deplatforming dramas of the last months (disappearance of @realDonaldTrump, etc)

August 13, 2021:

anonymous:
You said that before you die of old age you would implement a download zip of your whole site. That's fine but links to archived pages will still be broken if you die if you don't have someone to follow in your footsteps to maintain the site because the site will go offline or somebody will buy your expired domain name using it for another purpose. Do you have plans for someone to take over your site? I have thousands of archived pages, don't want that work to go to waste.

archive-is:
I do not think there are many people willing to maintain such a project, which is also unprofitable. All 4½ projects over there - (IA, Archive.today, Megalodon.jp, half-suspensed WebCite, and paid Pinboard.in) look running on energy and money of a single person each and likely will be greatly changed or shutdown by the heirs.

I could only advise to save everything locally to sync your documents with your own lifespan. Do not rely on clouds.

daveymames:
You don’t need many people mate, just a small amount of people is all that’s required. I for example would be willing to accept a passing of the torch. I would fund it with my own money and allow people to donate. I’m planning a site similar to Archive.org of my own that allows uploading via torrents so you can upload big files which is hard to do on archive.org and it bans people who don’t keep 1TB of stuff permanently seeded. This way I don’t need to waste money on storage.

How much does hosting cost you per month at the moment?

archive-is:
about ~$2600/mo of pure expenses on servers/domains, not counting “work time”, “buying laptop/furniture”, etc. ($100…300/mo covered by donations + $300…500 by ads)

I’d suggest starting with pdf/djvu archive:

• It is of demand: people here often ask about archiving pdf/djvu and are particularly interested in archiving from another website rather than uploading (for some vague legal reasons).

• Unlike archive.is, it is more a blob storage and fit to “store me a terabyte” model: there is no need to develop and support own file formats and its renderers.

• There is a ready-made dataset to rescue and get some press attention on: Sci-Hub.

• The mission is more about “save forever“ than our “keep a page online after the original took down or altered“.

archive-is:
Also, https://docs.softwareheritage.org/ is a storage-heavy initiative which would need extra mirrors and crawlers. I need it as a user, especially immutable weekly snapshots of whole language repositories (such as maven.apache.org, npmjs.com, crates.io, …)

January 28, 2022:

anonymous:
Do you have anything prepared for the fate of the archive in the event of your death?

archive-is:
It is an overly optimistic assumption that there will be no risks before I die. Many projects (including at least two in this area: peeep.us and webcitation.org) stopped working long before the death of the people behind them. Many projects pivoted following the money. In addition, there are many critical points (e.g., domains) that I have no control over.