Here are couple of examples that I prefer on iOS.
Soulver - Android has no equivalent, awesome calculator.
Notes - Android does not have a simple notes app. iOS' app also syncs/backs up to Yahoo.
Music - iOS' music app is just leaps and bounds better than anything Android has to offer.
GPS - Third party GPS apps are much better on iOS.
Photos - The default app is much better, cleaner without any extra nonsense effects. Also displays pictures on the map.
Tunebox - Dropbox music streamer, couldn't find anything like this for Android.
PhotoSync - Nothing like this on Android. Awesome app.
PinDrop - Again, nothing like this on Android.
SongExporter - Again, nothing like this on Android.
Instacast - None of Android's podcast apps come close.
OPlayer - An awesome video player. DivX, XviD, MKV, etc... plays them all. Also, you can play videos from your SAMBA(Windows) share over the network... i.e. Share a folder with movies from you Windows machine, connected with your iPhone and stream movies. Haven't found a player on Android that does that.
SuperList - There is Mighty Grocery List on Android but it's just not as good.
Converter+ - Awesome converter.
Skype - On iOS it is better.
Calculator app? There are 4 I can think of that are the same or better than iOS versions...
Tip Calculator
Scientific Calculator
RealCalc Scientific
Notes?
ColorNote Notepad, better than iOS simple because I can post a widget of my notes on my homescreen. Invaluable feature
Gnotes - Syncs with Gmail...
Music?
Poweramp - nothing on iOS compares.
GPS?
Google Maps Nav - Better than all third party apps because I can manage my maps on my desktop.
Photos?
Jelly Beans stock photo app is on par with iOS. But you could also DL Quick pic which is excellent also.
Dropbox music player?
MusicDropNPlayLite for Dropbox
Photosync?
I agree, there isnt anything like it on Android. MoPhotos give similar functionality tho (Compat with Eyefi and Lightroom)
Video Players? HAHAHAHA
MX player
Moboplayer
VLCPlayer
I could go on and on...you obviously haven't spent much time looking with Android...