Который является самым быстрым в MySQL PHP-или MySQLi?

Вам нужно создать другую таблицу для хранения результата вывода, в моем примере я назвал ее outputresult (user, score) :

Declare     @duser nvarchar(30)
Declare     @duser2 nvarchar(30)
Declare     @dscore int

DECLARE cur1 CURSOR FOR
select distinct [user] from TOP3s



OPEN cur1

FETCH NEXT FROM cur1 INTO @duser

WHILE @@Fetch_Status = 0 

BEGIN

Declare cur2 Cursor FOR
select top (3) [user], score from TOP3s where [user] = @duser order by [user], score desc
OPEN cur2

fetch next from cur2 into @duser2, @dscore

WHILE @@Fetch_Status = 0 

begin

insert into outputresult values(@duser2, @dscore)

fetch next from cur2 into @duser2, @dscore

end

close cur2
deallocate cur2


FETCH NEXT FROM cur1 INTO @duser

end

close cur1

Deallocate cur1


--you can run this query to check the output:
select * from outputresult