The "new" way, as mentioned, has nothing to do with SQL 2008. EXEC has been available for quite some time. It's also - in most cases - a Very Bad Idea.
You lose parameterization - meaning you are now vulnerable to SQL Injection. It's ugly and error-prone. It's less efficient. And it creates a new execution scope - meaning it can't share variables, temp tables, etc. - from it's calling stored proc.
sp_executesql is another (and preferred) method of executing dynamic SQL. It's what your client apps use, and it supports parameters - which fixes the most glaring problem of EXEC. However, it too has very limited use cases within a stored proc. About the only redeeming use is when you need a dynamic table or column name. T-SQL does not support a variable for that - so you need to use sp_executesql. The number of times you need or should be doing that are very low.
Bottom line - you'd be best off forgetting you ever heard of it.