outlook.com
I have a Gmail account. Let's call it 1234@gmail.com for example's sake. I've recently created the very same address on Hotmail. It's exactly the same as Gmail address – 1234@gmail.com
But whenever I try to send an email to this address – only Gmail version receives it. Why does it work like that? Addresses are exactly the same but only Gmail version receives mail.
Use Gmail. In Gmail, you can "Archive" old mail messages that you most likely don't want to see anymore to free the inbox from clutter; but the messages will still be there if you go to "All Mail" (or search).
When you log in into your Hotmail client, you should be able to go to Options and then choose Upgrade to Outlook.com
It also should not matter, what you use as login to your Windows Live account - it can be even GMail.
Best Answer
Because what you've created is a login, not an email address. Messages to a Gmail address will only go to Gmail servers. You need to set up email forwarding from Gmail to Outlook.com.