Office Online (Word, Excel, OneNote,...) is always not enough functioning in comparison with desktop application. Thus, the advanced features if edited on desktop application will become read-only on Online version.
For example: you can create an equation on word desktop and you can view it on online and never be edited.
However, there are some features can support on desktop application and there is no need to be editable on web application. For example, you need to set the password protect for any section in OneNote, for sure it is not available on Online but you can do on desktop application and sync to cloud. It will work fine on web application after that.
Conclusion: for being time, we should work on both web application and desktop application in order to use all the advanced features on desktop application because they will work properly on web application.
2) OneNote
Attachment File: each of attachment is available only 18MB. (*)
Audio Record: each of records is available only 3 minutes because of limitation from (*).
For the very first using the OneNote from Office 365, you will get an encountered error. To avoid the error when you open OneNote from Tiles of Office 365, you should go to OneDrive then create a new document with OneNote. From then, you can open OneNote from Tiles without any error.
3) OneDrive for Business
The best function in OneDrive is syncing the data from cloud to local device. I like this feature very much. It can help me work without internet connection and it can sync later. Or I can work from home (or anywhere) then automatically sync to cloud and I can continue working at any office from my end. However, not any folder names can be worked with OneDrive. Basically, on the cloud you can create the folder name with any legal characters, but sometime it does not work with local folder.
If you bypass this error and (forget) don't fix the folder name on cloud, your new data is never synced after that.
There are many questions from my trainees about the syncing function. It is very strange with the difference data between home and working office. Nobody knows or cares about the error when OneDrive component shows up on the desktop and normally user closes and leaves the reason.
Remember check and delete/rename the illegal folder name on cloud before sync the data.
Verify your folder name is here https://msdn.microsoft.com/en-us/library/windows/desktop/aa365247(v=vs.85).aspx
4) OneDrive for personal
With this version, you could not sync from cloud to desktop and limit storage is 5GB data.