Mobile Safari is very polished. I like how reliable the reader mode is. I like that it now does ad-blocking. On the other hand the web apps feel more integrated in Android. For example Chrome on Android does notifications now, so for example I could just use Facebook on the web and get push notifications. Also Android does alternative browsers, so Android has Firefox and Firefox has real extensions, including ad-blockers. Mobile Safari is really good though.
In terms of UI, Androids notifications are much better, as in they are reliable, they get grouped, you get shortcuts to act on them or you can dismiss them easily. On iOS the notifications are broken and the "unread" indicators are completely annoying. On iOS I also miss the Back button. They added sort of a hack lately for Safari, so you can return to the previous app from Safari. Along with double-tab on home, a pattern emerges ... they keep adding hacks as a substitute for the lack of a Back button. As a consequence of this, one of the things I hate on iOS is how every app opens its own web view. I mean, don't you just hate that?
Skype on my iOS is broken. It simply doesn't ring if the app is inactive. This is probably a bug, but it's also a bigger problem related to iOS. iOS is killing inactive apps, so it has special hooks for apps that need to be awoken by messages. This leads to weird effects - like Dropbox is unable to backup my photos in the background, because it cannot stay alive long enough to do it. And I've lost some photos that way, as I've reset my phone thinking that Dropbox managed to back me up. It's also weird to pause and then resume my music or my audiobooks. As resume doesn't necessarily work remote-controlled through your headsets as you have to wake your phone up first. Actually the behavior is inconsistent. It really depends on whether iOS managed to put your app to sleep or not. The upside of that is that the iPhone's idle mode is very efficient, but given my usage patterns, I haven't seen an overall improvement in battery life.
On the apps ecosystem, I feel Android has better apps. This may sound like heresy, but it's true, with Android having the benefit of a stronger open-source ecosystem. They finally unified the design under the material design guidelines. And with Marshmallow they finally fixed the permissions system, though iOS has the benefit of not having such a broken permissions model for such a long time. So for instance on iOS I felt comfortable installing Waze, but not on Android - thankfully that changes with Marshmallow.
iOS does better at out-of-the box standards being supported. It supports CalDAV and CardDAV for example. For Android you need special adapters that need to be bought for CalDAV / CardDAV and Google should be ashamed of themselves. On the other hand on Android just about anything is extensible, so support for CalDAV / CardDAV synching can be added by buying some available apps.
To sync my iPhone with my desktop I need to use iTunes. I hate iTunes with a passion, I really do. With Android I can just plug it in to my computer and just copy/paste some files in a folder.
Related to UX in general, iOS apps are good, except when they are not. For example RunKeeper on Android is more usable than RunKeeper on iOS, because on iOS you have to tap on things that don't seem tap-able. And for iBooks to not do bookmarks for audiobooks is a total screwup for a company like Apple.
On my iPhone I do like that I get SMS messages on my MacBook through iMessages and phone calls through FaceTime. That's pretty sweet. On Android I've used PushBullet but it's not the same. On the other hand I don't like feeling locked in Apple's ecosystem or in anybody's ecosystem for that matter. So I'm enjoying my iMessages and my FaceTime, but I try not to like it so much :-)
I think I can go on :-)