you are right , i guess blockchain is not particularly clear if there are major differences between both options/accounts ( i have backed up the recovery phrase long time ago and i also access blockchain account with password) i think they want to appear like a service that honor users ownership more than they really are and trying to make you think of important changes done to enhance security to continue use it.
If you want to access your currencies, pay attention to the recovery phrase. The main difference between it and the password is that the password is to access the account, and you can restrict this access either through two-factor authentication or a white list of the IP address.
The recovery phrase is the best option. The reason for this is that if the service stops suddenly, the password will not help you recover the account.
i have exodus wallet but not regularly using it i remember when i was sending crypto the wallet controlled which minimum amount allowed to be sent , it feel like commercial wallet and complete trash .
Exodus Wallet is a closed source wallet and there are some issues related to the security of your wallet seed. The best alternative to it is ----->
Unstoppable wallet, read Bitcointalk user experiences
[1]i like how blockchain.com is web based flexible and lightweight wallet takes low fees doesn't require client to download the whole blockchain . however i start to worry if i cannot access due to technical and security issues . then i shouldn't use this wallet again .
SPV wallets doesn't require client to download the whole blockchain and have better onchain fees estimation.
[1]
https://bitcointalksearch.org/topic/unstoppable-wallet-user-experiences-5436273