Hi Rajesh,
Our recommendation for most customers is to use the internet path for Office 365 traffic as ExpressRoute is inherently complex to implement and invariably the internet path provides the optimal method in terms of cost and complexity. You also may want to think about connectivity which is required over the internet, for example if you move Exchange or Skype Hybrid endpoints to be accessible over ExpressRoute, they are then not reachable to your users or other entities you want to expose them to publicly. As an example, if you move Autodiscover to be only exposed over ER then your users would have to VPN back into the corporate network to get their mail in some scenarios.
Even when a customer uses ExpressRoute, we generally recommend inbound (MS to customer) connections are kept on the internet path to keep the service availability the same and also simplify the routing model.
From a security standpoint, we publish the IPs used for the service so access can be restricted to Microsoft endpoints where appropriate.
Hope that helps,
Paul