Browser: In terms of browser, Safari >>> Chrome in terms of mobile browser. On desktop I'd take Chrome anyday, but right now the browser option in Android is terribad. The old AOSP browser was decent but to me it had rendering issues and wasn't perfect either. Chrome has great rendering and great text wrap and seems to format pages correctly, but the app is laggy, slow, and also a memory hog. Not to mention there's tons of reports across Google forums regarding battery drain.
I use a combination of Dolphin + Chrome, but it's still not perfect. When I open Youtube links in Facebook, it somehow opens the browser. If I select Dolphin, it will open mobile Youtube. If I select Chrome, then it reprompts me to open the Youtube app. I therefore can't take advantage of Android's "default app" option. I either default to Chrome so that Instagram links and Youtube links can open properly, and then I won't get Dolphin which is a much better browser overall, or I use Dolphin as the default browser, and the links never open properly.
It's kinda frustrating. You can argue that Safari is simple, but it does its job. Its fast, and has always rendered nicely since day 1, and webpages are properly formatted for mobile view and the text wraps nicely. The AOSP Browser has sucked a lot for this, and it wasn't til more recent builds of Chrome in the past year that the browsing experience on Android got to be decent.
Keyboard: Then we come to the Android keyboard. Til this day I'm not sure if Google gets it or not, bu the Android keyboard to me has taken a step backwards in the recent days. The text prediction and correction til this day still pale in comparison to the iOS keyboard back in 2007. Google's been slow to add features like multi touch and better prediction.
Today, the default keyboard is far too big. I was wondering why on my Nexus 4 I always missed the space bar. It's because the rest of the keyboard is so "tall" now that in order to hit the upper letters, my thumb's natural position wasn't hitting the space well enough. As a result I wouldoftentypelikethisintextmessages and then have to go back and fix it all. It didn't really figure out what was going on til recently. I decreased the height of my keys using a 3rd party keyboard (Kii) and realized that I was typing a lot more accurately. Meanwhile, the typos were still not getting caught as well... at least not as well as the iOS keyboard.
All I wish for was a solid tapping keyboard that could improve on the areas that Google missed out on. Before you name the dozens of 3rd party keyboards out there, I've tried them all. Swiftkey until recently forced you to use that hideous numpad layout. And even if you got used to it, I didn't, which is why every other smartphone platform uses a numrow layout. Swiftkey is also slow and hideous too. Other keyboards out there like Kii are customizable but lack in the prediction/auto correct capabilities. The same can be said for my previous keyboards like Better Keyboard and Smart Keyboard Pro. I recently found TouchPal X which is nice in prediction and autocorrection, but a numpad keyboard?!?!? It's frustrating.
And on the tablet front, in 2013 I searched through Swiftkey, Kii, Smart Keyboard, etc. and everyone had a phone optimized keyboard, not a tablet keyboard. Only the AOSP keyboard offered the backspace button at the upper RIGHT of the keyboard like an iPad and a real keyboard. That makes more sense on a Nexus 10.
It's frustrating. I've been searching for a solid keyboard for Android since day 1 and I still have not found it. It's not like the iOS keyboard is perfect, but it's a far better default app than the Android keyboard. I'd be ok sacrificing custom replacements if the default app was pretty good to begin with.
tl;dr: Out of the box, Android is lacking, and even if you can use 3rd party replacements, they may not really address all the problems. Everyone's in it to show off their new method of typing or doing things. It doesn't necessarily address shortcomings from the stock app.