SQL - Max Vs Inner Join

The answer to your question is to try both methods, and see which performs faster on your data in your environment. Unless you have a large amount of data, the difference is probably not important.

In this case, the traditional method of group by is probably better:

select u.user, max(p.price)
from table1 u join
     table2 p
     on u.uniqueid = p.uniqueid
group by u.user;

For such a query, you want an index on table2(uniqueid, price), and perhaps on table1(uniqueid, user) as well. This depends on the database engine.

Instead of a join, I would suggest not exists:

select u.user, p.price
from table1 u join
     table2 p
     on u.uniqueid = p.uniqueid
where not exists (select 1
                  from table1 u2 join
                       table2 p2
                       on u2.uniqueid = p2.uniqueid
                  where p2.price > p.price
                 );

Do note that these do not do exactly the same things. The first will return one row per user, no matter what. This version can return multiple rows, if there are multiple rows with the same price. On the other hand, it can return other columns from the rows with the maximum price, which is convenient.

Because your data structure requires a join in the subquery, I think you should stick with the group by approach.