I just recently had my BB upgraded to an iPhone for work. For personal use, I use an Android. I've only had my iPhone for less than a week and as it is a work phone, I only have a few apps that I use on both so far. These apps are Pulse, Google+ and Yahoo Weather.
With Pulse, it seems that the Android app has a few more features. For instance, on Android I can configure Pulse that certain sources should be opened in the web browser mode. I cannot do that on the iOS version. I have to open the article and then use another few taps to open the app in web mode. Other than that, both are pretty much the same.
With G+, I also noticed that I could do something on Android that I cannot do on the iOS version. On Android, I can reply to a comment of a post and it will automatically tag the author of the post. I cannot do that on the iOS version. Other than that, they are more or less the same.
For Yahoo! Weather, I found that the iOS version had a feature not available on the Android version. The iOS version had some written synopsis of the forecast in the details section where it says what to expect in the next day or so. This written synopsis is not present in the Android version. Other than that, both are the same.
A few general observations as a whole is that Android uses a back button on the bottom right of my Galaxy S3. It makes it easy for me to go back to the previous screen. I often use it. There is no such back button on iOS apps. Generally, in iOS there is a button somewhere on the screen that you can tap on to bring you back to the previous screen. iOS apps also seem to have alternative gestures to go back to the previous screen depending on which screen you are on. In some G+ screens, if you are at the bottom, you can try to scroll down more by dragging the screen up and then release and it goes back to the previous screen. In Pulse, you side swipe from the left edge inwards to go back on certain screens. These gesters only work on certain screens and not all screens and appear to be inconsistent across different applications.
Another general observation is that with iOS, there seems to be a lack of a landscape mode sometimes. In Android, there seems to more places in apps where I can turn the phone to landscape orientation. In iOS, there are fewer instances that has a landscape mode.
As for smoothness of apps, I'm comparing a Galaxy S3 and an iPhone 5S. The iP5S is a year and a half newer than the SGS3. I would expect that the iPhone would be smoother. The difference to me is noticeable, but not by much. The SGS3 is a really good phone even though it is now 2 generations behind the latest models from Samsung. What surprised me about the iPhone 5S is that I had experience lag a few times while typing on it. I noticed that I would hit a few keys, the phone would suddenly pause for a second and then catch up. On my SGS3, I use Kii when typing in landscape and I don't experience lag on it. I experience a little lag using Swype whenever I put a double space after a period.
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