Like the rest of the world, I switched from the Blackberry to an iPhone. Here are my thoughts on functionality.
There are a bunch of native blackberry functions that required paid apps. Most are cheap.
How do you create an calendar entry in another time zone? Well, you can't, not without an additional app. I use Week Cal to replicate functionality (in particular handling appointments in other time zones). It isn't possible to get an iphone to nag you as much as a blackberry does automatically. Touching the screen on an iphone dismisses a reminder, which is easy to do inadvertently, and there is no snooze on calendar appointments. This carries over to using the phone as an alarm clock -- I often want the sound turned down for calls and such, but then have to remember to turn it up for the alarm clock because it is the same volume setting. Vibrate also worked better on the BB -- I often miss vibration reminders on the iphone. This is the single worst feature -- if you need to be nagged to not miss appointments, you're going to miss appointments. Week Cal's biggest defect is that it makes it hard to dial a phone number in an appointment -- you click on the number and navigate through several screens, and even then it doesn't support "x" as a prefix to extension, so I wind up needing both the native calendar and Week Cal.
I also use the $1 app "Later" to make quick reminders -- making a calendar entry is slow and easy to put on the wrong day or even the wrong year, and Later is great for a quick reminder in an hour or at a particular time.
I used my blackberry as a travel alarm clock. The problem with hotel alarm clocks is that every one is different and you have to watch for things like the alarm set to radio and the sound turned down or the time set to AM rather than PM, or the alarm set to go off at 6PM instead of 6AM. So I just ignore the hotel clock and used the BB, which worked fine. The iphone isn't as good about this and you are stuck with the native app because if you use a third party app, you have to remember to turn on the sound -- if the sound if off (my usual state), a third party alarm won't ring. The native alarm clock is OK, though.
Free blackberry travel is great. There is nothing like it on the iphone cheaply. I wound up paying for Tripit Pro ($50/year) to replicate, although tripit pro is actually better in some ways, especially web sync, which I wind up using frequently. Tripit free is only partway there, and in particular won't notice when flights reschedule like BB Travel or Tripit Pro. Tripit Pro will suggest alternative flights, which BB wouldn't do.
Initially it wasn't possible to sync tasks and notes (memos) directly and I used Toodledo and a free sync program. However, the sync program broke with Outlook 2010 and created over 1000 copies of my appointments before I noticed the problem. Fortunately, Apple updated to support over the air sync of tasks. I still have to use itunes for notes, but as I don't change those too frequently, that works ok for me.
By the way, iTunes for windows is the worst program I use on a regular basis and one of the all time worst I've encountered. Don't let it run automatically and keep it off except for synching. Don't let it manage your music. Just say no.
Free Blackberry news RSS reader is quite good. I use RSS a lot; it is my major source of news. I've tried Feedler, Reeder and Byline and in the end Byline is the only one I use. The great thing about Byline is not only does it cache the stories, but also the linked webpages, so that you can read the full story on the airplane with no internet connection. Reeder is the most popular, but Feedler is better, because of more effective caching of the stories. On a plane, Reeder often came up empty -- all I would have were titles. I like Byline better than the BB news reader. (BTW, I use FeedDemon on the PC and this keeps the stories visible synched, so once I read a story it disappears from all my devices, a major advantage of RSS.) I occasionally browse through flipboard for its nice interface, but I prefer the RSS title list to having to page through stories.
The BB had no native weather app -- good ones were $10 -- and the native iphone app is quite good. This is the only case where the native iPhone app beats a native blackberry app.
Blackberry's google maps was much better than the iphone maps (which is provided by Google). The thing I really want here is to see all my (starred) favorites on a screen and be able to add starred locations. I now have a bunch of map programs. The native one won't do it although it finds stuff well; the best you can do is to see 2 locations, which you do by plotting a route between them. Google has a web app but it doesn't work very well and makes it very hard (perhaps impossible) to star a location. This was really easy on the BB. A product called "off maps" does this and in addition stores the map on the device (which means you can download the map on wifi and then use it when wifi isn't available which is great) but it can't find an address, only a street or intersection (idiotic). Tripadvisor has maps but you are out of luck choosing what to display. So it seems to be impossible to perform my normal use case of identifying 15 or 20 locations in a city I want to star and showing those, and only those, on a map. This was easy on the BB with google maps, and when traveling, I wind up using three different mapping programs, a major nuisance. I doubt Google is supporting the BB in the future, so the superiority of the BB platform in maps is probably temporarily.
On the plus side of the iphone, there is a bunch of functionality just not available on the BB. Identify constellations, find hikes inside national parks, a compass, TripAdvisor's city guides (which you can download and browse off-line, terrific and free), IMDB (this is terrific), kindle app (way better than I expected), translation, skype (that is a biggie, especially internationally), stock market programs and a decent scientific calculator. None of that list are more than $2 and most are free. I can even FTP a text file (html) and edit it and FTP it back. The BB was terrible for browsing but the iphone isn't bad at all -- pinch and zoom is a really nice invention. The iphone uses a lot of data, probably 10X the blackberry. I watched a couple of movies on long flights. This is fine -- the iphone has a beautiful screen -- but personally I would rather read on a kindle.
Mail is much better on the iphone, although the iphone often takes a long time to sync a message. This is the fault of AT&T (problem vanishes with wifi) but it is worse on the iphone than the BB. But my biggest frustration is that it just isn't good for calendar reminders.
Then there is the battery life. I can't make a day, not close, even after turning down the screen and turning off location services and bluetooth. Some days I need two charges during the day. I carry an external battery from New Trent that insures I can make a whole day even if I talk 8 hours and browse intensively. I could run a mapping program constantly on the BB for 8 hours or more; on the iphone this is more like 4-5.
I have put the Nuu keyboard on my iphone, $50. It has its own battery and goes about a week between charges, even with backlighting. (The backlight and Bluetooth are on only when you slide it out.) I think this makes me 3X faster at typing than the one finger on screen keyboard, and that is not quite as fast as on a BB. It makes the phone quite fat. I can type ok on the virtual keyboard in landscape mode when I'm sitting, but when walking I make too many mistakes and the keyboard helps a lot.
Music does sound better on the iphone than on the BB. I have high bandwidth mp3s -- 256K -- but on a BB you couldn't tell.
So the iphone isn't a slam dunk but overall I probably like the iphone better. If Apple would fix reminders, I would be a lot happier with the iphone.