You can use Boolean under vBulletin's builtin search as well.
Fulltext
Pros
Less PHP resources used because the indexing takes place in MySQL.
No need to maintain the postindex and word tables which can take up a lot of space.
Natural Language and Phrase searching is available.
Can Sort by relevancy for better results
Default search in vBulletin's latest versions.
Can support more searches per minute.
Searches can take better advantage of MySQL's query caching.
Cons
Less Flexible Indexing, especially on Shared Servers. Changing parameters requires shutting down MySQL, dropping indexes and rebuilding them.
Fewer control parameters within vBulletin.
Rigid Stopword list as an external file.
vBulletin Builtin Search
Pros
Not reliant on your MySQL version.
Can be easily manipulated in the Admin CP including adding words under the minimum character limit or changing that limit.
Cons
Resource heavy, especially building the index.
Indexing must be done before post is inserted to database and can result in errors on overwhelmed systems.
Search Results can cause database errors if there are too many hits.
Large tables must be maintained manually for proper usage.
No Natural Language or Phrase based searching.
Easy to bring down large boards with multiple searches.
Fulltext
Pros
Less PHP resources used because the indexing takes place in MySQL.
No need to maintain the postindex and word tables which can take up a lot of space.
Natural Language and Phrase searching is available.
Can Sort by relevancy for better results
Default search in vBulletin's latest versions.
Can support more searches per minute.
Searches can take better advantage of MySQL's query caching.
Cons
Less Flexible Indexing, especially on Shared Servers. Changing parameters requires shutting down MySQL, dropping indexes and rebuilding them.
Fewer control parameters within vBulletin.
Rigid Stopword list as an external file.
vBulletin Builtin Search
Pros
Not reliant on your MySQL version.
Can be easily manipulated in the Admin CP including adding words under the minimum character limit or changing that limit.
Cons
Resource heavy, especially building the index.
Indexing must be done before post is inserted to database and can result in errors on overwhelmed systems.
Search Results can cause database errors if there are too many hits.
Large tables must be maintained manually for proper usage.
No Natural Language or Phrase based searching.
Easy to bring down large boards with multiple searches.