Having clause vs subquery

The two versions are functionally the same. Well, the second is syntactically incorrect, but I assume you mean:

select * from (    select team, count(min) as count    from table    group by team) twhere count > 500

(You need the alias on the calculation and several leading databases require an alias on a subquery in a FROM clause.)

Being functionally equivalent does not mean that they are necessarily optimized the same way. There are often multiple ways to write a query that are functionally equivalent. However, the specific database engine/optimizer can choose (and often does choose) different optimization paths.

In this case, the query is so simple that it is hard to think of multiple optimization paths. For both versions, the engine basically has to aggregate teh query and then test the second column for the filter. I personally cannot see many variations on this theme. Any decent SQL engine should use indexes, if appropriate, in either both cases or neither.

So, the anwer to this specific question is that in any reasonable database, these should result in the same execution plan (i.e., in the use of indexes, the user of parallelism, and the choice of aggregation algorithm). However, being functionally equivalent does not mean that a given database engine is going to produce the same exeuction plan. So, the general answer is "no".