I seem to be swimming against the flow here , but I've actually moved from web-based to a mail client years ago !. A good mail client like TB is superior to accessing your mail through the browser for the following reasons :
1- Offline work ! , you can only read/search/write mail to outbox while you're online ! - when am away with no internet connection I can read,search and compose messages , and synch in a couple of minutes when I'm connected.
2- Multiple accounts , all log in directly without having to log in or open tabs..etc.
3- No Ads when using your yahoo , gmail or hotmail accounts !.
4- No browser scripts or malware reading your cookies and hacking your accounts - especially hotmail.
5- I share my emails (TB profile) on different OSs/computers , so they're all synched , including attachments
and the list goes on... It's just much more convenient.