Okay first of all, giving the CEO/CTO access to plaintext passwords is just plain stupid. If you are doing things right, there is no need for this. If a hacker break your site, what's stopping him from attacking the CEO next?
Both methods are wrong.
Comparing the hash of a received password against a stored hash means the user sends his plaintext password on every login, a backdoor in your webapp will obtain this. If the hacker does not have sufficient privileges to plant a backdoor, he will just break the hashes with his 10K GPU botnet. If the hashes cannot be broken, it means they have collisions, which means you have a weak hash, augmenting a blind brute force attack by magnitudes. I am not exaggerating, this happens every day, on sites with millions of users.
Letting users use plaintext passwords to login to your site means letting them user the same password on every site. This is what 99% of all public sites do today, it is a pathetic, malicious, anti-evolutionary practice.
The ideal solution is to use a combination of both SSL client certificates and server certificates. If you do this correctly, it will render the common MITM/Phishing attack impossible; an attack of such could not be used against the credentials OR the session. Furthermore, users are able to store their client certificates on cryptographic hardware such as smart cards, allowing them to login on any computer without the risk of losing their credentials (although they'd still be vulnerable to session hijacking).
You make think I'm being unreasonable, but SSL client certificates were invented for a reason...