You're kidding, right?
How on earth could webmail be more secure? If client mail is set up properly, everything is always, automatically encrypted. With webmail, if you 'accidentally' get rerouted to the non-encrypted site, your whole email life is a wide open book to even the lowest-wrung hackers.
Also, unless if your computer is a mess of spyware (In which case, nothing is secure, no matter what), your personal information is more securely stored and archived on your own computer, than the 'cloud', where nobody actually knows where your data is, or who has access to it.
Also, unless if you forward all your email to a single account (spreading each email across multiple servers, in multiple locations, from multiple companies, with the number of eyes who can see your email multiplied), handling multiple email addresses is a pain.
I have about 20 various email addresses, as well as my own email server. I could install a webmail server, but it wouldn't be as quick, convenient, or secure as just using a client.
I can also read and compose email when I don't have an Internet connection. Try THAT with webmail.
Maybe for the average user, and especially those who don't know what an IMAP or POP is, webmail is great. However, for powerusers, and those knowledgeable enough to know what's more secure, clients are the way to go.
I stopped using webmail a long time ago.
Web email is much more secure then using an email client.
You can use several different web based emails and import your other email accounts. Like Gmail, Outllook, Yahoo, etc. they will scan attachments before you download to your hard drive, spam emails are not opened unless you open them, with email clients they download everything directly to your hard drive including infected attachments and spam. Then the filters will delete the content.
Gmail allows you to open attachments in Google Documents cloud instead of having to download them to your hard drive.
I stopped using email clients a very long time ago.
Thanks.