I guess note number one about MyISAM to Innodb migration is warning what Innodb is very slow in COUNT(*) queries. The part which I often however see omitted is fact it only applies to COUNT(*) queries without WHERE clause.
So if you have query like SELECT COUNT(*) FROM USER It will be much faster for MyISAM (MEMORY and some others) tables because they would simply read number of rows in the table from stored value. Innodb will however need to perform full table scan or full index scan because it does not have such counter, it also can’t be solved by simple singe counter for Innodb tables as different transactions may see different number of rows in the table.
If you have query like SELECT COUNT(*) FROM IMAGE WHERE USER_ID=5 this query will be executed same way both for MyISAM and Innodb tables by performing index rage scan. This can be faster or slower both for MyISAM and Innodb depending on various conditions.
In real applications there are much more queries of second type rather than first type so it is typically not as bad problem as it may look. Most typically count of rows is needed by admin tools which may show it in table statistics, it may also be used in application stats to show something like “We have 123.345 users which have uploaded 1.344.656 images” but these are normally easy to remove.
So remember Innodb is not slow for ALL COUNT(*) queries but only for very specific case of COUNT(*) query without WHERE clause. It does not mean I would not like to see it fixed though, it is pretty annoying.