Chrome on iOS is rubbish.
...because the Chrome guys are daft? Nope. ...because it's Apple's playground, and they don't want to play, so they've deliberately ('not deliberately') made it so anyone using their engine is a 2nd class citizen, and can only build a poor user experience.
(https://code.google.com/p/chromium/issues/detail?id=423444 for the meta bug if you're interested)
What makes it rubbish? I remember using it when it was released and I switched to it as my main browser instantly. At the time I felt it was better than Safari, if not only for the top bar being smaller and/or hidden, something Safari did not do at the time. It also had the "request desktop" which is invaluable at times.
Currently I use Safari but it's because I haven't bothered since I use the iPhone browser for almost nothing.
and its not Chrome's fault. Apple do not allow any other web browser on iOS, so Chrome is just WebKit except you don't get the same javascript engine as Safari does.
I stubbornly continue to use it because I want my history and bookmarks to match my desktop.
I also use my devices jailbroken, and there are fixes for the Javascript engine. That being said, I mostly used it without them, and even when I did I noticed no difference. Again, probably because I use the iOS browsers very little.
You can use UIWebView, the older interface. The biggest problem is that its JavaScript engine is slower than Safari's, and does not JIT compile code (according to Apple, this is for security reasons). I've also seen complaints about scrolling performance.
You can use WKWebView, the newer interface. Its JavaScript engine does JIT, and it boasts 60fps scrolling. Unfortunately, it's missing several features detailed in the bug, including a way to clear and manage cookies, custom URL handlers, POST request bodies missing in certain cases, etc.
One would hope that the WkWebView bugs and omissions will be addressed in future iOS versions, but today is not possible to make an iOS browser that works as well as Safari.
This is very similar to what Windows Phone is doing as well. You can't download FF or Chrome on their phones, just other poor IE clones. Granted, IE has come a long way and is pretty decent on Windows Phone, but if I could use one browser across all my devices, I'd be a bit happier.
Windows started the war when they locked out native third-party code development on the Windows Phone 7 platform. Then in subsequent findings, Chrome lamented they can't get enough privileges with Metro app development to make it work and Mozilla knows MS doesn't want to further their platform - so a sort of stalemate at this point, and a loss to Windows Phone users.
Sources:
Mozilla: No plans to release Firefox for Windows Phone 7 (March 2010)
http://www.zdnet.com/article/mozilla-no-plans-to-release-fir...!
Google Has ‘No Current Plans’ to Bring Chrome to Windows Phone (August 2014)
http://www.omgchrome.com/no-current-plans-to-bring-google-ch...
