GMail is perhaps the best web-based mail client out there. Outlook Web Access, by the way, is the worst ("user-hostile" is how I would describe it). Though I find it relatively speedy and similar in feel to a local mail client, it still doesn't beat a local mail client. Why?

• Natural Feel Web-based applications make compromises to the interface to make them work.* Too often, webmail feels rather kludgey. To put something in a folder, for instance, I have to click a check box next to a folder, select the folder (or label in GMail), then click move (or archive). Or, I could just drag-and-drop in a local client.
• Offline Access This was a bigger deal to me ten years ago, when access was via a modem and my only phone line. However, being able to read mail offline, or draft out a new message, is still something nice to have.
• Integration with Other Applications It's nice to be able to click "Share via E-mail" in iPhoto. It's nice to drag-and-drop attachments.
• Extensions A variation of the previous point. There are tons of extensions for most mail clients to add capabilities. The one that jumps to mind is encryption (either PGP or GNUPG), though other ones (Growl for its fans, for instance) are there too.
• Browser Independence I know mail is going to work the way I want it to, regardless of IE, Firefox, or Safari.
• Multiple Accounts at Once Just what it says. For instance, I have multiple accounts with one webmail provider. I can look at it all at once with Mail.app. I'd have to log in/log out to each account otherwise.

Can I find the right work-around, process, or browser extension to make these features kinda work. I just find that a separate mail application generally works better.

IMAP is really something that levels all this out. I can have my local client do the heavy lifting, but the view on the web and on my phone track what's going on. Again, it doesn't solve for everything, but I think it means I don't have to make a choice.

*I admit Google does a better job than most.