I've been running Android P for a while now on my original Google Pixel. I ran the beta for a few weeks, and switched to using my Pixel as my main phone around the time P was officially released.
Here are some of the good and bad things I've noticed about it.
Disconnecting Bluetooth accessories
In P, tapping or long-pressing on items in the control centre thing no longer offers extra detail for that control. Now, you can simply turn things on and off from here, or long press to open the actual settings app. Before P, disconnecting a Bluetooth accessory while leaving Bluetooth enabled would consist of long pressing the Bluetooth icon, then tapping the accessory you wanted to disconnect. In P, I have to long press the Bluetooth icon to open settings, tap the cog next to the accessory I want to disconnect, and tap disconnect. Then I'm left in the settings app, rather than in the context from where I initiated the change. The whole thing is more awkward and disruptive than it used to be.
Do not disturb
I always loved how Android's Do Not Disturb feature let you set it for a certain time, after which it would automatically turn off. On iOS, you only have the option to turn it on or off (though this is changing in iOS 12).
Before P, you could turn on DND from the control centre, which would set it for an hour, and you'd see options automatically to adjust how many hours it was on for. In P, I haven't figured out a way to change this dynamically. You can change the default length of DND when it's turned on manually in settings, but I'm yet to find a way to change the length of DND each time I turn it on.
Update: This is actually possible! You can turn on a setting so that every time you turn on DND it'll ask you how long to set it for, which is exactly what I wanted.
Before switching back to my Pixel I'd been using an iPhone X. My main reason for using the X was because I hate the physical home buttons on iPhones, so the new swipe-based navigation really attracted me. Both OS's let you swipe across the bottom of the screen, from left to right, to quickly switch between open apps. The current app is the right-most app, and the rest of your open apps are lined up to the left, just like normal app switching.
What's weird about the iOS implementation is the app you were just in can end up to the right. So if you just switched to a different app and want to switch back, you need to swipe right and left to check where that app went. After a short period, the current app ends up being right-most, but you can never know for sure how long that period is. On Android, the current app is always the right-most app, so you know you can always swipe to the right to see all open apps to the left.
Android's version is also more strict. It snaps to each app as you swipe, whereas on iOS you can swipe as much or as little as you want, and it's up to you to line up with the app you want to switch to.
Shortcuts to recently used apps
One new feature of P that I love is when you swipe up to show the app drawer, there's a two-stage swipe, and the first stage shows just the multitasking view and your 5 most recently used apps. This is really handy for jumping between apps quickly.
If you keep swiping to the app drawer, you'll see app slices mixed in with app icons. Slices are little parts of apps you can work with—shortcuts, basically. I usually see two from Telegram: one for my conversation with Josh, and one to start a new conversation. I use Telegram a lot, every day, so it makes sense that these would be suggested.
Since the iPhone X did away with the home button, Apple had to find a new way to take on-device screenshots. The iPhone X uses a similar process to my Pixel: the on/off button (or side button, as Apple insists on calling it) and volume up. My Pixel uses volume down and the power button.
Here's the difference though: on Android, I have to hold these buttons for a second or two before my screenshot is taken. On iOS, the screenshot happens immediately. And because the side button and volume buttons are on opposite sides of the phone, I take accidental screenshots just from holding my phone all the time.
Apple's making a change to help with this problem in iOS 12, but the best they have to offer is not taking screenshots if your phone's screen is off (why was that possible anyway). So it won't help much at all.
Update: Someone mentioned a handy tip I'd missed, which is that you can hold down the power button, and alongside the option to restart your phone, you'll also see an option to take a screenshot. This makes it much easier to take screenshots with one hand, without adjusting your grip.
Any major OS update comes with lots of small changes, so there are probably plenty more I haven't noticed yet. These are just a few that have stood out most based on how I use my Pixel.