Marco Russo and Alberto Ferrari make a comparison:
DAX offers a rich set of functions, some of which overlap in their functionalities. Among the many, two functions perform grouping: SUMMARIZE and GROUPBY. These are not the only two: SUMMARIZECOLUMNS and GROUPCROSSAPPLY perform similar operations. However, the article is about SUMMARIZE and GROUPBY, as the other functions have many more functionalities, so a comparison would be unfair.
To make a long story short: GROUPBY should be used to group by local columns, columns created on the fly by DAX functions. SUMMARIZE should be used to group by model and query columns. Be mindful that both functions support both scenarios: both functions can group by model and local columns. However, using the wrong function translates into a strong decrease in performance.
Read on for a detailed explanation.