Todd and Sarov have provided great answers already. Just adding to that.
Small batch size also provides faster and more frequent feedback loops (or opportunities to react!), as it moves through its workflow or value stream. The faster a batch of work reaches the next stage of workflow or gets delivered to the customer, the faster it gets "reviewed" at each stage. Any defects or gaps in intended function (features or UX related) can be detected and corrective action can be taken. The larger the batch size the longer it takes to do so. To the extent you define "improved performance" as "shorter time to market with the right product", shorter batches improve performance.
This video demonstrates this quite effectively - https://www.youtube.com/watch?v=JoLHKSE8sfU
As for your question - "Does this all mean that 2 batches of 10 tasks are executed (as a whole) faster that 1 batch of 20 tasks?" - you have to also look at your own as well as your customer's cost of coordination and deployment for each batch. It is possible that your development and deployment cadences need to be loosely coupled to adjust to how often your customer can accept new versions of your product. If they cannot accept new versions more than once a quarter (typical corporate IT policy), your releasing weekly or monthly may not mean higher performance for them.
However, if you deploy your weekly/ monthly releases on a staging server and let their users play around with new features and give you feedback, which helps you improve the quality of the product delivered at the end of the quarter, now that is improved performance. The Kanban Method refers to this in its 2-Phase Commit capability. SAFe refers to this as "Develop on Cadence. Deliver on Demand".
In my years of experience in software, to my mind, the biggest challenge that software teams and users have is not knowing what the user really needs till they start to see what they actually get. The faster the dev team can get something to the user, the faster the users can see and react to it and the faster they can start to converge on building what they really need. The smaller the batch size that a team can deliver, the higher their performance.