I will be referring to Outlook/Hotmail/Live email service as Outlook.
Both Outlook and Gmail are way better than Yahoo email. Because Yahoo email does not offers email auto forwarding for free.
However, Outlook is better than Gmail when it comes to auto forwarding email. This is because if you want to setup forwarding automatically for Gmail, you will need to give Gmail the verification code that was sent to the recipient, and this is not good, because I need to setup auto forwarding rules to many different co-worker and customers. And therefore, it is impossible for me to go around bothering people for confirmation codes.
Therefore, if you need to setup auto forwarding then I suggest that you use Outlook.
