My hope is that Google will take the best of both worlds and make something better. So in order to help facilitate that, here's my high level best/worst lists for each.
[update: 12/19/2015]: Russian translation available here thanks to Vlad!
What Chrome OS Does Well
Simplicity: Chrome OS is simple and intuitive. I would feel absolutely comfortable giving a chromebook to my mom or dad and be confident that they could surf the web and check their email without any problems.
Multiple Users: At first I didn't like that you had to log in to a Chromebook with a GMail account. But after using the Pixel for 3 years I think it makes things easier. My wife and I both share the Pixel and we do so with zero hassle. Logging in and out is fast and intuitive and there isn't an extra username/password that you have to remember. When friends come over and want to surf the web they can pick up the Pixel and start using it right away using their GMail account (and it seems almost everyone has one).
The Web: It should go without saying (but it won't) that an OS built on top of a browser should be good at surfing the web. And it is. Web based email works great. Streaming media like Netflix, Amazon Instant Video, and etc work great. Chrome OS just works when it comes to the web.
SSH: Surprisingly, Chrome OS's Secure Shell program works great and supports key based authentication. This makes using Chrome OS to work on servers simple and efficient.
Native Development Support: If you're a developer you can get shell access with crosh and use crouton to create a chroot to another flavor of Linux (like Ubuntu). Once you have a chroot setup you'll have access to the full suite of developer tools that Linux has to offer.
What Android Does Well
Niche Apps: I've come to rely on apps like KeePass, Owncloud, and Baby Connect in my day to day life. These apps go with me wherever I go and give me instant access to important information. Android is a very friendly environment for niche apps.
Mobile First Experiences: Instagram, Maps and Navigation (disclaimer, I work at Amazon on Maps), streaming media (these have web counterparts but they're lesser experiences than the mobile apps IMO because they're cluttered with display advertising), and a whole plethora of other apps that are built first for mobile and second for the web.
Games: While I'm not a big gamer, Android does games well. Games like Angry Birds, Fruit Ninja, Plants vs Zombies, Cut the Rope, Solitaire, Sudoku, and etc all run great and are fun on Android.
Contacts, Calendar, and Email: The native apps for contacts, email, and calendar work great, sync great, and are easy to use.
Switch to developer mode: Developer mode isn't turned on by default in Android. But it's really easy to enable. Just tap on the system version several times and you've unlocked the power of being a developer.
What Chrome OS Doesn't Do Well
Apps: Chrome is pretty horrible for apps. The HTML5 based apps I've used are clunky and not very functional.
Switch to developer mode: Switching to developer mode on Chrome OS is awful. It requires you to wipe your machine when switching in and out of developer mode. While booting up in developer mode you're presented with a terrible screen telling you that OS Verification is off. If you hit space bar you wipe the machine. Switching in and out of developer mode just isn't easy.
What Android Doesn't Do Well