The big advantage of Office 365 is if you want to use Outlook as your client on your PC. Outlook works best when using the EAS protocol to talk to the mail server. Hotmail doesn't support EAS for desktop clients. (Strangely, it does support it for mobile clients.) So you have to use IMAP on the desktop, which doesn't work as well, and also doesn't give you task and calendar sync. EAS enables the full vision of cloud email, since your phone and desktop Outlook client will always be magically fully synced. So Outlook on the desktop doesn't go well with Hotmail.
If you are happy using the Hotmail web client on your desktop (and plan to always be connected to the Internet), you won't have this sync problem, and so you would have no reason to subscribe to Office 365 or equivalent.
Outlook does not use EAS. EAS is a mobile protocol for synching.
I'm pretty sure, Outlook uses RPC over HTTP to sync with Exchange, which is completely different.
Hotmail does not support IMAP. It supports POP3 and DeltaSync - the latter of which is implemented in Outlook Connector/Outlook 2010 and in Windows Live Mail. Hotmail has never supported IMAP. Exchange, however, does support IMAP as well as OWA which can be used to sync email to some clients (i.e. Blackberries via BIS can use OWA to sync Exchange mailboxes).
You can use Windows Live Mail and Outlook to Sync Windows Live data. The main issue -some- people have is the way it partitions off Windows Live data from your main Outlook data. People just want to have everything in one place, instead of having to duplicate it due to the way it's handled by Outlook.
This can easily be solved, by people who have no hard preferences, by simply switching to Windows Live Mail. For others, paying for a hosted Exchange account and using that is a worthy work around. I personally think it's a waste of cash. I did have a Hosted Exchange account for a while, though. Just didn't seem worth the hassle to me. If you use different platforms concurrently the Exchange account can free you from having to have accounts on multiple services (though that's a bit harder to do these days
).