Microsoft Office Online is very much like the Offline version of Microsoft Office from a visual perspective minus a few options in the File Menu that are exclusive to the Offline version. As a suite it is 99.98% the same as what you would get in the Home Offline version & the Home & Personal Office 365 editions.
|Office Online Apps|
In Office Online you get Microsoft Word, Microsoft OneNote, Microsoft Excel, Microsoft PowerPoint & OneDrive. In the Online version of Office gone is Microsoft Access for Databases, and Microsoft Outlook is through the outlook.com service. This setup is very similar to Googles Online Office Suite where there is Google Drive, Google Docs, Google slides, Google Sheets & instead of a note taking app there is Google drawing with Email handled though mail.google.com or inbox.google.com for the lucky few with access to Googles new Inbox Email service.
Office Online Apps
All the Office Online Applications have all the same features as their Offline counterparts meaning that Office Online is instantly familiar to anyone who uses Office Offline in a business or Educational setting. With the Chrome Web Apps that Microsoft launched for Online suite a few months back it means that the Industry standard Office suite is now available on Linux and Chrome OS devices in Application styled Windows that don't remind you that you're using a web application and not Just Windows and Mac making it possible to use Office on a device that doesn't run the suite natively in a distraction free Window without having access to a Windows or Machine or Mac that you can Remote Desktop into.
The best part of Office Online is that it's free making it ideal for someone that doesn't need Office all the time, making it ideal for the occasional times that you need word for something that Google Docs can't handle, like if you need to attach your CV to an Online Job Application where most of the time it has to be in Microsoft Word format.
Outlook.com can handle more than just Microsoft Accounts (Hotmail, Live & outlook.com), but having to use outlook.com means that you need to login with your Microsoft Account instead of being able to just get instant access to all of your accounts when opening the web app or going on the website, but for a full version of Outlook that you can use on any machine it's worth having to login all the time especially when it's free.
I'd definitely recommend Office Online for anyone who needs occasional access to Microsoft Office or even to anyone with one of the paid options that needs Office on a machine that doesn't have Office installed, or even on a public computer where you don't really want to be saving documents onto the computer. As for outlook.com I'd recommend that to anyone who only wants to access a Microsoft Account, for anyone who wants to use it like the regular Outlook then it really depends on weather you don't mind having to login all the time to get access to all of your accounts without having to have multiple browser tabs open.
If you use a Chromebook then Office Online is the best way to get Microsoft Office on your Chromebook, even if you've got a Windows Laptop or Desktop that you can remote Desktop into to access the Offline versions of Office I'd go the Office Online route and put all that saved money to good use upgrading the Storage on OneDrive, unless you need access to Microsoft Access for any reason then you're probably better off going with an Offline version of Office.
I've got the Office Online web apps installed on my Chromebook, but they get used very rarely as I tend to go with the Google Office suite. the last time I used one of the Office Online apps was when I used PowerPoint to create the Chrome Buzz banner, that's how raerely I've found the need to use Office Online.