I have been a Tripit user for a few years and have been very happy with it. I am currently on a trip associated with work, and the agency that books travel for the University uses a service called Sabre, which owns Tripcase, and my plane reservations were automatically saved as a Tripcase trip, so this gave me an excuse to compare the two apps.
Essentially, these apps both allow you to track the details of a trip that you might otherwise store in a bunch of notes or emails: plane and hotel reservations, restaurant invitiations, meetings, theatre tickets. Everybody has their own system of lists for such things, I suppose, but Tripit actually helped me learn to organize things into one place, while not losing the ability to pull out the crucial bits–what is my flight number? what is the hotel address for the cab driver?–quickly without sorting through bits of paper or lots of calendar entries. I wouldn't travel without one of these apps loaded with info.
Both apps have iPhone apps and web viewing and entry. I have found that both apps sync quickly with new info I enter on the web. You can share your Tripit plans with other folks who have signed up with Tripit (free), and there is a business version of Tripit (which I haven't tried) that allows folks in an office to keep track of each other's meetings and travel plans, and, I presume, allow the office staff to make changes as new businessy appts or travel plans change. I usually travel alone, but when I have traveled with others Tripit really helped us keep reservations that we made separately straight. Tripcase allows sharing too, but one difference is that those with whom you share your trips get updates by email when you make a change to the trip. This is probably good for business travel or when an office staff person might be making arrangements for a group of people, but for the casual, just-let-your-family-know-where-they-can-find-you use, it is pretty annoying.
The absolutely dead cool thing about these apps is how easy it is to import information. When you get an email confirmation of a reservation from a hotel or airline, just forward it to firstname.lastname@example.org or plans @tripcase.com, and the apps/service parse the information into readable information with the pertinent details–times, dates, confirmation numbers, contact info, addresses in the right places in your Trip. I'm sure there is some protocol the original sender's message has to use for this to workI dont know what it is), but I have not had an airline or hotel reservatiob import failure yet. The way this information is rendered in each app is quite similar, though I find Tripcase a bit easier to read (big fonts for these middle aged eyes). With TripIt Pro (annual fee involved), you can check flight status and get alerts. TripCase did this in the background on this trip, though if the reservation had been made with a non-Sabre agent, I can't say if I would have gotten those alerts. My contacts also got updates on my trip from TripCase (as emails for them, phone alerts for me)-when the plane left, when it landed.
When importing other information, such as emails regarding theatre tickets or dinner reservations, the apps differ a bit. You can send these emails to plans@ for both of them, but only Tripit knew what to do with the information from a ticket vendor, though I had to tweak it a bit, and it also included all the garbage about not being late and and liability exclusions and all of that other junk noboby reads or wants in confirmations for theatre tickets. I had to add the info manually in TripCase. In both programs, adding activities is similar, though TripCase annoyingly requires an end time for each activity (if you just want to note you need to meet someone at noon, it is irritating to have to change the the default end time of the next day or the end of your trip for each event in your trip.
One of the handy features is that both apps will automatically grab maps for you if you have entered an address for your activity.
One feature Tripit has that TripCase does not is the ability to attach photos to your activities. It is nice to be able to add a photo of the front of a hotel or the poster from a show you are seeing. Or just a pic of a friend who is appearing in MacBeth at Lincoln Center:
That is hardly a necessary feature, but it is fun when you are planning a trip about which you are excited, or if you are on a tour where you are staying in a number of places, and you need help keeping them straight.
All in all, if you are using one of these apps, there doesn't seem to be enough difference in them to make an argument for switching. TripCase renders very nicely on the iPhone, so it is especially nice if you just want to use the app to keep your connections handy and your confirmation numbers all together. For a quick check, TripCase has the edge. For a bit more flexibility in what you track on a trip, including images of where you are going or who you need to see there, I still like TripIt. And if I don't reup for TripIt pro, I can use another free app to track my flights and get updates on departure and gate changes.