For international searches, ie searches aimed at retrieving prior art from all the major industrial countries, the advanced level is the one to use because it contains the PCT minimum documentation, classified in detail according to the latest version.
For national searches, ie searches directed at retrieving documents from a specific country, the core level will usually be sufficient. Some of the smaller patent offices will anyway classify their documents at core level only. If you are sure that the office in question classifies at advanced level, then you can use it for a national search. However, for any search where the number of documents is not very high, a core-level search might still be more appropriate, since it will give more hits and be less sensitive to minor variations in classification philosophy.
Once you have performed an advanced-level search, you should consider doing a second search at core level, because the documents of some countries will only be classified at core level.
Even for international-type searches, it may sometimes be a good idea to use core-level classifications to limit your search to a broad technical field, eg when combining classification and text searches (documents classified in the advanced level will in any event automatically be retrieved, since they are also allocated corresponding core-level classifications via an automated procedure).