First, and most obviously, you need to consider the constraints of both platforms. The primary constraint when you are designing an iPhone app is screen size. You have a smaller "canvas" to work with, and that constraint means that you can't overload the UI with an abundancy of controls and information. Not to say that you can "go nuts" when you are designing for the iPad, but you do have some more area to work with… you shouldn't overdo it there, either.
(Another general piece of advice is to get a good understanding of the UI conventions and controls for both devices by studying the iOS Design Guidelines from Apple… so that when you decide to "break" any of these conventions you will at least be able to do so in an informed intelligent way).
Second, if you are building an iPad version of an iPad app, you may want to "reverse engineer" the experience of the iPhone app, to identify what works and what doesn't. What are the core tasks that the app lets the user do? What can be done to enhance or improve these tasks when designing them for the iPad? Test the existing app with users, even if it's just casual "guerrilla testing." You may find that tasks and user needs that work perfectly fine in the mobile context on an iPhone make no sense on the iPad.
Case in point: I design banking and financial service apps, and one of the big new features that all the newer apps are providing is called "Remote Deposit Capture." What is that, you may ask? It's basically the ability to take a photo of a check and deposit it using a mobile banking app. It's universally well regarded by customers and a "delighter"… but it's hardly used on the iPad versions of different mobile banking apps. Why? My theory is it's just easier to take a picture with an iPhone than with an iPad, and the "awkwardness" is reducing usage and perceived value. You may find many features that "make sense" on the iPhone that don't on the iPad.
The opposite is also true, of course… there are going to be some features that don't work in an iPhone app but would work great on an iPad. Any feature that involved "drag-and-drop" as an interaction model, for example.
And for goodness sake, don't use the added screen real estate to add more features and information just because you can! Approach the design of the iPad application with the same discipline you would use when designing a small-screened mobile app. On second thought, use MORE discipline because the temptation will be greater.
Finally, a thought on behavior and context: Many of the best apps on the iPhone are designed to support "quick" behavior – you go in, you do something, you get out. This is because the iPhone is a mobile phone and when people use it they are often… well, mobile. The iPad is a different creature altogether. Though I HAVE seen people walking around city streets using an iPad to do something as they traverse crowds, it's a rare occasion – people do that with iPhones all the time. iPads are used a lot more for "browsing" and so the best apps on that platform provide a simple interface to consumer and interact with content.
Obviously, everyone and every app is different… but you should really look at what people want to do and where they do it first and foremost… no matter what platform you are designing for.
See question on Quora