Both of these projects are in the early stage. Both have proven crypto entrepreneurs behind them, and based on that fact, both have exploded into the top ten most valuable crypto currencies without yet having a product.
I'm very confident that both project will enjoy outrageous success, but I've listened to enough of Cardano's Charles Hoskinson, and EOS's Dan Larimer and that I think I grok how each regards its advantages and the other's weaknesses:
Cardano camp:
• EOS will have scaling problems just like everyone else. They aren’t designed from the ground up for a billion people and it’s hard to make changes to a system already functioning.
• They did not do the hard work of proving that their systems, including Delegated Proof of Stake, are cryptographically secure against a precisely defined threat.
• They are not following the most rigorous procedures for designing and deploying software. This is a bad way to build something as important as financial infrastructure.
EOS camp:
• We may not have theoretically limitless scaling like Cardano, but we will have enough to cover planet Earth. That’s enough . . . for now.
• All code is fallible. Your kidding yourself if you think otherwise. Our human-first approach aligns incentives correctly and gives the right people authority to react to problems and fund their resolutions.
There are other competitors too, of course. Including but not limited to: NEO, NEM, Enigma, Stratis, Qtum, Waves and many, many, many others. Despite my efforts, I have not kept up.
Perhaps I should also summarize
Ethereum's Vitalik Buterin's criticism of EOS:
Short version: “Delegated proof of work” is not really decentralized because there are only hundreds of nodes that do all the work.
Short version of how I understand Dan's response: There are thousands of nodes TRYING to do the work, and it is up to holder of the currency to nominate / approve / vote for who does the work. This is a better alignment of incentives that relying on miners (74% of whose capacity is in China, btw) and who are not even necessarily holders of large quantities of the currency they mine.
Short version of how I think Cardano's Charles Hoskinson would respond to the debate: You didn't invest in rigorously specifying your criteria and mathematically proving your security.
(Comments welcome. I'm trying to understand this complicated space.)