There are too many factors to consider before one could state that "Tableau's performance decreases with larger datasets".
I am aware that Netflix, Facebook, ExxonMobil, UBS (Speakers | Tableau Conference 2014) are using Tableau on production processes. The DW size managed by Netflix is around 10PBytes, but they are using presto read more here The Netflix Tech Blog: Using Presto in our Big Data Platform on AWS
My suggestion is to contact a sales account manager and discuss your requirements.
I understand. Thanks a lot!