MAX vs Top 1 - which is better?

1) When there is a clustered index on the table and the column to be queried, both the MAX() operator and the query SELECT TOP 1 will have almost identical performance.

2) When there is no clustered index on the table and the column to be queried, the MAX() operator offers the better performance.

Reference: http://www.johnsansom.com/performance-comparison-of-select-top-1-verses-max/

They are different queries.

The first one returns many records (the biggest a_date for each event_id found within a_primary_key = 5)

The second one returns one record (the smallest a_date found within a_primary_key = 5).

Performance is generally similar, if your table is indexed.

Worth considering though: Top usually only makes sense if you're ordering your results (otherwise, top of what?)

Ordering a result requires more processing.

Min doesn't always require ordering. (Just depends, but often you don't need order by or group by, etc.)

In your two examples, I'd expect speed / x-plan to be very similar. You can always turn to your stats to make sure, but I doubt the difference would be significant.