It all depends on the complexity of the data you are working with. If you are taking about data transformation (converting to timestamp, replacing quote, ...etc.) then maybe groovy is the way to go. JSLT has some function that can you help you accomplish this as well like string replace and parse-time functons but Im not sure that is everything. Im not sure where did you get the impression that the nifi community doesnt recommend using groovey and if you find an article about that please share. I think its more of an issue with your Boss not wanting you to do any scripting to avoid not having this supported by others than you.

The processor is there for you to use. Actually there is a dedicated processor for groovey called ExecuteGroovyScript. I think the ExecuteScript processor might get deprecated since its redundant. The only issue that  I can find that warns about this processor is the fact the script is getting compiled for every flowfile and that might get expensive and impact the performance if you have a big script and working with large data volume. To avoid running into those scenarios, Nifi provides other alternative like InvokeScriptedProcessor (using groovey as well) or develop your custom processor in java (.nar) where the code is compiled once and done.

The jslt processor also re compiles the script but it uses caching to avoid having to do that every time. In terms which performs better: groovey or jslt? Im not sure and I have never tested but you can do some stress testing and let us know :).