In PostgreSQL, exactly what you'll get here depends on the underlying table, so you should use EXPLAIN ANALYZE on some sample queries against a useful subset of your data to figure out exactly what the optimizer is going to do (make sure the tables you're running against have been ANALYZEd too). IN can be processed a couple of different ways, and that's why you need to look at some samples to figure out which alternative is being used for your data. There is no simple generic answer to your question.
As for the specific question you added in your revision, against a trivial data set with no indexes involved here's an example of the two query plans you'll get:
postgres=# explain analyze select * from x where s in ('123','456');
Seq Scan on x (cost=0.00..84994.69 rows=263271 width=181) (actual time=0.015..1819.702 rows=247823 loops=1)
Filter: (s = ANY ('{123,456}'::bpchar[]))
Total runtime: 1931.370 ms
postgres=# explain analyze select * from x where s='123' or s='456';
Seq Scan on x (cost=0.00..90163.62 rows=263271 width=181) (actual time=0.014..1835.944 rows=247823 loops=1)
Filter: ((s = '123'::bpchar) OR (s = '456'::bpchar))
Total runtime: 1949.478 ms
Those two runtimes are essentially identical, because the real processing time is dominated by the sequential scan across the table; running multiple times shows the difference between the two is below the run to run margin of error. As you can see, PostgreSQL transforms the IN case into using its ANY filter, which should always execute faster than a series of ORs. Again, this trivial case is not necessarily representative of what you'll see on a serious query where indexes and the like are involved. Regardless, manually replacing INs with a series of OR statements should never be faster, because the optimizer knows the best thing to do here if it has good data to work with.
In general, PostgreSQL knows more tricks for how to optimize complicated queries than the MySQL optimizer does, but it also relies heavily on your having given the optimizer enough data to work with. The first links on the "Performance Optimization" section of the PostgreSQL wiki covers the most important things needed to get good results from the optimizer.