Great question OP.
To be honest, the iPad is an exceptional device. Having owned an iPhone since Gen. 1, I've been accustomed to iOS on a handheld device. Using an iPhone and it's features are great, don't get me wrong, but you always have that idea that you are on a "superior mobile" version of apps and web browsing.
I never understood the hype around the iPad since the beginning, as I thought that I already had everything it could do in my hand on my iPhone. After making my first iPad purchase a few weeks ago, Boy was I wrong!
Where the iPad excels in, is the UI. You don't have that feeling of using a "superior mobile" version of the Web, apps, docs., etc. The iPad is a lot more homey, intimate, a truly one on one experience. The web browsing as mentioned above by other members is by far the best browsing I've ever done. It's like using your desktop but much more intimate^. Full screen web pages, sharp crisp text, tabbed browsing; an elegant experience all at your fingertips.
Photos are FUN. Using a desktop there is time and management that is required. On an iPad, they are just there. You can easily edit them in iPhoto, email, tweet, etc. all with a click of a few buttons. Again, fun.
Most people who don't own both devices have the image of the same device with just a bigger screen. As proclaimed by azure247 above^. They couldn't be more wrong. The iPhone is a great product for what it does. And the iPad is a great product for what it does. They both differ in so many ways, and the UI, even though being the same iOS, vary greatly. As I mentioned above, it's a much more intimate and pleasurable experience. It's a desktop in your hand, not a cell phone.
In the end, the reason I have both is because they serve different purposes (although it may seem difficult to justify that claim) My phone is with me all day every day. I view it more as a tool. It has the web for info in an instant, local weather, Google maps.. Pretty much all useful tools. I use my iPhone as another tool for my workday. Now with my iPad, it pretty much took my MacBooks place. It's more of an at home device, a sit down and relax and read a book device. One where I can take full advantage of a desktop like experience all with my fingertips and the comfort of my couch or bed. And now with both the full iLife and iWork suites readily available on the iPad, It's an experience you have to take in yourself.
Oh and btw, my MacBook Pro gets used rarely now and my iPhone I only whip out when I need to make a call or when I don't have my iPad or when it's charging (which can seem like an infinity) Sad but true.