The problem with favoring sessions over cookies for 'security' is that sessions USE cookies to identify the user, so any issue with cookies is present with sessions.
One thing to keep in mind with the use of Sessions is data locality. If you plan to scale to more than one webserver at any point, you need to be very careful storing large amounts of data in the session objects.
Since you are using .NET, you will basically have to write your own session store provider to handle this, as InProc won't scale past 1 server, the DB provider is just a bad idea entirely (The whole point is to AVOID DB reads here while scaling, not add more), and the StateServer has a lot of capacity issues. (In the past, I have used a memcached session store provider with some success to combat this issue).
I would google for signed cookies and look into using that instead of either regular cookies or sessions. It solves a lot of the security concerns, and removes the locality issues with sessions. Keep in mind they come back and forth on every request, so store data sparingly.