Although desktop clients used to be the sensible choice for heavy email users, robust services such as Google's have made Web solutions completely viable. Nonetheless, after relying on Gmail for about eight years, I recently switched to a local application (Postbox). The decision came partly because I just wanted a change, but I had legitimate issues with Google's mail offering, including its sluggish POP3 fetch times, lackluster offline support, random latency fits and the occasional -- albeit forgivable -- downtime.
I always avoided local clients because Outlook made a lousy impression. It wouldn't play nice with Gmail over IMAP and it had too many useless features (useless to me, anyway). Part of the benefit of a desktop client is having more options, but that just made Outlook feel cluttered. Postbox's interface is less busy, yet there are tons more features than your typical one-size-fits-all cloud service. Having my mail locally feels faster, I don't have to worry about my password cookies expiring and offline access is as good as it gets.
Postbox isn't perfect though. While it offers superior filtering options, Gmail is smarter about handling spam without your help. Even with various filters, I still get tons of spam through my TechSpot address. It was also easier to configure mail across multiple devices when I had everything feeding into one Gmail account. I only needed one set of credentials versus four. Fortunately, this isn't an issue as I tend to use the same couple machines every day, but it might be enough to drive me back to Gmail if I switched regularly.
It's ultimately a compromise between customizability and convenience. I think I've settled on the former for now, but I wouldn't hesitate to make Gmail my primary mail hub again if my situation changed. How about you? Do you use a desktop client or Web service (or both) to access your email and why?