I would suggest that you do offer some kind of benefit to the users that have stuck with you during the beta period.
Based on my experience as a frequent beta user, its very frustrating to feel no appreciation from a company that you have provided a service to. During the beta period, those users are testing your software. Sure, they are also getting access to the service for free, but they are providing value to you as well (imagine if you had to pay enough testers to do what your beta users did).
By offering them a discount, you are likely encouraging them to go with the premium rather than free service in the future. As many companies based on the freemium model have found, it can be a bit difficult to convince someone used to getting a product for free to start paying for it. By offering them a discount (with a limited expiration on it), you could very well encourage those beta testers to be part of your long-term paid customer base.
This is all said without any knowledge of your cost/profit structure of course, so if would end up losing you money to offer enough of an incentive, I take back everything I just said.