Unless it's changed recently, a Class 2 Medical is more stringent than a Class 3. Class 1 is the highest standard.
When I started, the ATCO requirement in The U.K. was Class 1, for both NATS and non-NATS ATCOs. The was the same as for a commercial pilot, but with slightly more leniency with regards to the frequency of re-examination.
I think the change to a Class 3 for ATCOs came during the mid-2000s?