As far as a "cloud" webmail interface goes Gmail has the best search features (which probably contributes to why so many Slashdotters prefer Gmail), but the search features introduced into the Thunderbird 3.x mail client are the best of any e-mail interface. To even rival the customizability of searches that is available in Thunderbird 3.x would require one to be fluent with command-line commands like find and grep, but acquiring such fluency is temporally expensive.

Timothy (OP) says that he has already tried Thunderbird though, but since his first complaint is that moving the "hundred of thousands of emails" that he has hoarded over the past two decades between the email systems that he has already tried takes "forever to process", Timothy appears to have some unreasonable expectations regarding data sets that large (specifically in regards to migrating and indexing such sets).

For those who do not feel comfortable keeping their e-mails in the cloud, they could always use Thunderbird 3.x as the interface and administer their own IMAP server at home using software like Dovecot.

...That should have been the title of the article, considering that the high-speed pea-sized ferromagnetic meteorite was basically a bullet from the heavens. ...And God apparently has lousy aim.

My friend is a professional graphics artist, and he recently switched from using Photoshop to using GIMP. He likes GIMP better than Photoshop because he finds that GIMP is more "tweakable".