They have common syntax and generate similar results. The analytic functions in Advanced SQL Engine are expected to run with better performance because they are native to the database.
SELECT * FROM function_name ( ...
See Teradata Vantage™ - Advanced SQL Engine Analytic Functions, B035-1206.
SELECT * FROM function_name_MLE ( ...NTree and nPath are exceptions. You must append "@coprocessor" to these function names:
SELECT * FROM nPath@coprocessor ( ...
See Teradata Vantage™ Machine Learning Engine Analytic Function Reference, B700-4003.