iOS 9 is now upon us, available free of charge from Apple to anyone whose device can run iOS 8. On the surface it's a small step forward for the mobile OS – there's no drastic design overhaul to speak of and a lack of obvious game-changing new features – but dig a little bit deeper into the software and there's a stack of subtler tweaks that make the upgrade well worth it.

Unlike Google, Apple still updates its stock apps (Mail, Maps and so on) at the same time as the main OS, so there are some app-specific features to talk about: Apple Maps gets public transit information for a handful of cities worldwide, while Mail lets you annotate attachments and attach any type of file to an email for the first time.

For most people, these new tweaks might not get discovered for weeks or months, but we wanted to play around with them as quickly as possible. The transit information is particularly well done and intuitive to use – there are alerts when your bus is late – but why such a limited geographical roll-out? Presumably Apple can pay for access to the same databases Google uses.

The long-neglected Notes gets some love, with support for web links, photos, checklists and iCloud syncing. There's also a brand new News app for U.S. users, which works like Flipboard and brings you a curated 'magazine' of news stories (including Gizmag content) specifically formatted for Apple's mobile devices. Like most of the new features in iOS 9, they improve the operating system but are unlikely to have Android users switching en masse.

Across the OS as a whole, both iCloud and Siri receive some upgrades, which isn't a surprise – the market for cloud storage and digital assistant apps is fiercer than ever, with both Microsoft and Google making ground. iCloud is now a much more visible app and users are finally able to browse their files via an app on the Home screen.

We had mixed experiences with the new visible iCloud Drive icon. It doesn't show automatically, and though on some of our devices we got a message asking if we wanted to reveal the icon, on two other devices (iPhone 6 and iPad mini 2) we never got that pop-up and had to go into Settings if you to manually toggle it. iCloud may not have exactly the same aims as OneDrive or Google Drive or Dropbox (iCloud is still aiming for more of an automatic, background experience), but the Drive component is still lagging in terms of usability. This is a small step in the right direction.

As we heard when Apple unveiled iOS 9 in June, Siri is becoming more helpful and more proactive. The app is now more context-aware, able to understand what content you're looking at and where you are in the world when asking for assistance. Through the Spotlight search app, Siri makes suggestions based on your previous activities, which sounds a lot like what Google Now has been doing for some time.

The updates to Siri are particularly welcome: the app now feels like it knows something about you (like whether you're interested in the Miami Dolphins or just plain old dolphins). Of course there's a privacy angle but Apple promises all your data stays on the device rather than being ferreted back to advertisers, which is fine with us. The news stories Siri suggested to us weren't particularly relevant but presumably that improves with time.

Another new feature borrowed from Google is the option to add events straight to your calendar when they're spotted in an email (in the interests of balance, we should point out that Android has borrowed its fair share of features from iOS down the years too, dating back to the first versions). The email-to-calendar functionality is another small but useful feature that's going to make a difference if you're fully invested in the Apple ecosystem.

Perhaps the biggest upgrades are for iPad users. If you own an iPad Air 1 or 2, or an iPad mini 2, 3 or 4, you can take advantage of two new features: Slide Over and Picture-in-Picture. The former lets you swipe in from the right of the screen to show a second app in a special sidebar view, while the latter lets you minimize a video so you can use another app while it plays in a corner.

For owners of iPads with 2 GB+ RAM (iPad Air 2, iPad mini 4 and the upcoming iPad Pro), there's also Split View, a true multitasking environment where two apps can be viewed and used side-by-side. To activate it, you simply launch Slide Over and then drag the dividing line into the middle of the screen.

We tested Split View on both an Air 2 and Mini 4, and it could make the iPad a much more work-friendly device, once more apps are updated for it. Right now lots of Apple apps work with it, and a few early-updating third-party apps (like 1Password and Instapaper) as well, but many more are currently inompatible (Twitter, Facebook and TextExpander, for example, will be welcomed updates if or when they arrive).

And on older iPads, we found Slide Over to still be useful, even if you can't use both apps simultaneously.

In addition, all iPad iOS 9 users can turn their keyboards into temporary trackpads by pressing and holding with two fingers on the keys. This still won't make a touchscreen keyboard as good as a physical one, but it's a big step in the right direction, as text selection has long been a big pain in the keester on mobile devices.

We should also mention the low power mode, which shuts down a lot of background processes and can (Apple says) eke out another hour of battery life. Safari rather controversially now supports ad-blockers too, so you can browse the web more easily, and with less of a drain on your internet connection and battery level (and less money sent to content publishers).

One design tweak that will interest Android users is the introduction of a back button of sorts. When you click on something like a notification or link that pops you into another app, a "Back to [previous app]" message appears in the top-left corner. It's long overdue in iOS, and makes going back to where you came from as you jump from app to app much more intuitive (on iOS 8, you had to double-tap the Home button to bring up the multitasking view).

As soon as you start to use it, it makes perfect sense – and it does pose the question of why Apple didn't introduce it earlier. Much mobile device use involves jumping from app to app (opening a map from an address in an email, checking an Instagram picture from a tweet and so on), and having one uniform method for retracing your steps is really handy (that must be why Android has always insisted on it).

Apart from that, there are the usual under-the-hood improvements and tweaks, with Apple promising improved security, better battery performance and a more fluid iOS experience overall. And what's more, the keyboard now actually shows lower case letters when you're using lower case letters. The process of updating both apps and the OS itself has been streamlined in iOS 9 too.

Based on the time we've spent with iOS 9 on various devices, it does come across as slightly more responsive and intuitive, though you're not going to notice a dramatic difference. The new in-app features make sense – they already feel like they've been there a long time, which is a good sign – and we didn't come across any bugs, crashes or apps that failed to load. For the vast majority, it should be safe to jump on the iOS 9 train.

After you've upgraded and rebooted, you won't immediately see much of a change, beyond the new San Francisco font found everywhere from the Apple Watch to OS X 10.11 El Capitan; yet the improvements in iOS 9 are thoughtful, useful and well worth having for all Apple device users. The interface is more polished, and Siri is getting better all the time.

The new features are particularly worthwhile for iPad users, with Apple no doubt keen to make its slates (including the new iPad Pro) a more compelling proposition for buyers. But really anyone who owns an iDevice is going to find something useful here, even if there's no standout innovation that shifts the balance between iOS and Android. We might have to wait for iOS 10 for that.

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