The question really doesn't make sense to me, or to a lot of others, I suspect. Both are web mail services. You don't "use" one and store your mail on the other. You use whichever you like and store your mail on it. You usually access these services via their web pages.

I think Microsoft now calls Outlook Express "Live Mail client". You can use that with either service through IMAP. in either case, your email will be resident on the server unless you specifically download it to a local archive file and delete the server copy.

So, use Outlook Express/Live Mail if you wish, and choose whichever web service you like for your email provider.