With one scrum team velocity against itself over time it is easy - just number of points per sprint. But how to measure performance of several scrum teams against each other?
Scrum teams are unique and shouldn't be compared to one another in terms of productivity using things like velocity or story point sizing.
Where you may gain some benefit from comparing scrum teams is in their Agile-Scrum adoption/maturity and practices.
Does one team always meet it's commitments and the other does not? Why? Can team 2 use something that team 1 does, to help team 2 meet commitments? Maybe.
Always remember when you compare Agile-scrum teams, that what works for 1 team doesn't necessarily work for team 2. Don't fall into the trap of blindly implementing processes or policies across teams without understanding the underlying problem you are trying to solve.
Respect scrum ceremonies and basic building blocks like story definition and estimation. The rest is up to the team to self-organize.
Comparing Scrum team performance is easy: measure each team's ability to meet delivery commitments.
The purpose of Scrum is to enable teams to estimate reliably and communicate effectively about development roadblocks so that they can make reliable delivery commitments to each other and customers. The best Scrum team will have the best commitment delivery rating.
A bad Scrum team is one that is unpredictable across iterations (sprints) and can't be relied on to deliver promised software features.
A good Scrum team delivers what it promises, when it promises so that customer and funding decisions can be made with confidence.
Need clarification - what performance are you attempting to measure, and for what purposes? For example, are you attempting to benchmark quality, or business value delivered, or adaptability to changing requirements, or cross-training, or...?
Most important would be what are the primary benefits you hope to benchmarking teams against each other - team performance is a multi-variate problem in so many dimensions that it can be difficult to get to a useful set of metrics which can be used effectively.