Monero isn't just claiming this though. It actually delivers on its promises. It's actually private, authorities are having trouble tracing it. Criminals are already switching to Monero. Transactions are fast and the fees are low. It's mineable by ordinary CPUs, no centralized ASIC/GPU mining operations in China. Since mining is more decentralized, nobody opposes improvements to the Monero blockchain like the bitcoin and ethereum miners do.
> at least 10x better
Monero is pretty much infinitely better. If any coin is positioned to unseat bitcoin it's Monero. If there's any sanity left in this cryptocurrency market this will happen one day.
Ethereum: Market Cap: Fr 261,435,750,490 Volume: Fr 39,931,852,584
Its not like Bitcoin is standing up there alone. Sure still far stronger, but the times where its only bitcoin and the others is likely over.
This is the case of having a better technology doesn't matter, Bitcoin came at a very lucky time and also grew organically for many years and had arguably the fairest coin distributions (most coins nowadays are shilled very heavily by it's developers and investors). It's also the most secure and well-known.
Because of those things, it'll be very difficult if not impossible to unseat Bitcoin when it comes to store of value/currency. Bitcoin also sees development in form of lightning network. For all other use cases, I think eth covers most bases and has also developed a very large network of users and developers.
So whatever next big crypto project comes needs to be not just "better", but like at least 10x better.