There is a solid Exchange client app, Touchdown for Exchange from NitroDesk, that works with the Droid, but only by lying to Exchange about ActiveSync policy support for on-device encryption and password requirements. The tech support staff at NitroDesk told me I shouldn't use the app with the Droid because of that bug. Touchdown is a good app, with iPhone-like capabilities such as setting which folders to keep synced, and it even lets you set away notices, which the iPhone Mail app can't do. However, it doesn't display your Sent folders, which is a major gap.
For calendars, the Droid syncs to Exchange calendars (even if your server uses ActiveSync policies), but you can't accept invitations. On the iPhone, you can -- unless the invite came in as an e-mail attachment on a non-Exchange account.
The Droid displays Exchange calendars in a separate app, so you can't see your personal and corporate appointments at the same time. In the iPhone, you can see all or any calendars at once. (The HTC Droid Eris, which has extensions to the stock Android UI used by the Motorola Droid, also lets you see your Exchange and personal calendars in one app.) The one calendar advantage the Droid holds over the iPhone is that the Droid lets you select which personal calendars to view simultaneously; with the iPhone, you see all or just one.
If you intend to use your Droid for Exchange access, don't tell Verizon -- don't inform the salesperson that you'll be using Exchange or corporate e-mail, and don't call tech support with Exchange questions. Otherwise, Verizon will add $15 to your monthly data plan.
The iPhone can sync to Outlook on the PC, as well as iCal and Address Book on the Mac via a USB connection. The Droid cannot. Both devices support Gmail syncing (which you can use an intermediary to sync with Outlook and iCal/Mail/Address Book), though the Droid can do so over the air without a $99-a-year MobileMe account, as the iPhone requires.
Both the Droid and the iPhone let you view common attachment formats such as Word, Excel, and PDF; the Droid bundles the Quickoffice viewer apps to do so, while Apple has its own document viewer baked in to the iPhone. But neither can handle zipped attachments. I give Droid a nod for letting you save attachments for use with other apps, which the iPhone still can't do. (The iPhone can save image attachments.)
In its address book, the iPhone lets you jump easily to contacts by tapping an onscreen letter, such as T to navigate to people whose last names begin with T. Or you can search for someone in the Search field by tapping part of the name. The Droid lets you type a letter on the physical keyboard to jump easily to contacts; if you are using the touchscreen, you have to go through a menu command to search just your contacts (the standard Search button searches both the Web and the Droid). Both the Droid and the iPhone let you designate favorite contacts, which are handily displayed in a separate pane, and both have call log and phone dialer panes in their Contacts apps.
The winner: The iPhone, thanks to its real-world Exchange support and better calendar capabilities. The Droid's only advantages -- the ability to save e-mail attachments and over-the-air syncing with Google Gmail -- can't overcome its deficits.