Yeah, I prefer a one stop solution that caters for all 4 email accounts I'm using.
My primary email client is actually Outlook on PC so it's on my PC where I decide what mail to delete and what mail to keep for future reference. My email backup resides on my PC in the form of an Outlook pst file. I also find Outlook native search features to be vastly superior to any web based solution.
Space isn't an issue either. Neither is data so, by default, I want all mails to download in all their intended glory...