kj38, i believe yahoo email is usually set up for POP forwarding meaning when you sync emails from yahoo email to a client (eg, iphone or outlook), emails are pulled from the yahoo server but when you delete them that info is not communicated back to the yahoo server. Gmail is set up on IMAP which allows that two-way communication.
But I believe for the iphone, yahoo email does sync via IMAP, you just have to fiddle with the advance settings on your iphone to make sure emails are deleted. Under Settings --> Mail, Contacts, Calendars --> Accounts (yahoo account) --> Advanced --> Mailbox Behaviors --> Deleted Mailbox, make sure On the Server, Trash is selected. When you delete emails on your iphone, it will now send them to the "Trash" folder on the yahoo server instead of the iphone (ie, moving the email from the server & iphone inbox to the yahoo server trash box.
Either way, neither gmail nor yahoo will allow true syncing of your email, calendar, and contacts across iphone, email server, and a PC/Mac unless you have an Exchange server account or MobileMe. I just understood this myself and am now considering getting mobileMe. For example, even with the setting described above, if you were to go to your yahoo or gmail account and then delete emails on the online version after having iphone pull them, it would not delete the email on the iphone. That type of true syncing, I believe, requires Exchange or MobileMe.