I struggled with both these approaches for more complex queries than those shown, because the subquery approach was horribly ineficient no matter what indexes I put on, and because I couldn't get the outer self-join through Hibernate
The best (and easiest) way to do this is to group by something which is constructed to contain a concatenation of the fields you require and then to pull them out using expressions in the SELECT clause. If you need to do a MAX() make sure that the field you want to MAX() over is always at the most significant end of the concatenated entity.
The key to understanding this is that the query can only make sense if these other fields are invariant for any entity which satisfies the Max(), so in terms of the sort the other pieces of the concatenation can be ignored. It explains how to do this at the very bottom of this link. http://dev.mysql.com/doc/refman/5.0/en/group-by-hidden-columns.html
If you can get am insert/update event (like a trigger) to pre-compute the concatenation of the fields you can index it and the query will be as fast as if the group by was over just the field you actually wanted to MAX(). You can even use it to get the maximum of multiple fields. I use it to do queries against multi-dimensional trees expresssed as nested sets.