Since you synced your gmail account and still went back to using it online, perhaps you simply prefer that method.
For me, I like using Apple Mail for a few reasons:
1)
Consolidation. I have a few different accounts (gmail, school, ect.). It's nice to have all of them checked at the same time and gathered in one place. No mailbox forwarding or anything like that, all of my mail is organized and distinguished according to which box it belongs to.
2)
Speed. I do not like waiting on a web browser when there is a natively running piece of software that does the same thing. No loading the page, clicking on links, waiting for another page to load, ect.
3)
Availability. I like to have my emails available for review 24/7. There are times when the internet may not be available to me, or it is just extremely slow and difficult to deal with. It's nice to have everything accessible
offline, plus there's no waiting for attachments to download, should you need them from the message after getting it the first time.
4)
Integration. Everyone likes when people get along the way that they are supposed to. If using Mail (or Eudora/Entourage), you gain the ability of sending an email strait from numerous pieces of software (Example: Sending a document or media directly from its respective program) as well as being able to distribute notifications from you calendar (iCal) and produce bulk messaging lists (Address Book).
5)
Feel. Last, but perhaps not the least, I love when things fit in with my operating system aesthetically. I probably don't need to explain this one, Apple Mail looks like it belongs in OS X because it
does belong to OS X.
Just about all of the above can be accomplished in some way, shape, or form via a browser-based client, but I submit that it wouldn't be as easy (or dare I say, fun?)
Like I said in the beginning, if navigating to your email in the browser works for you, that's great. It's just nice to have options.