Search Differences: Basic and Enterprise

Basic Search Center: Contextual Search within sites and lists.
Enterprise Search Center - Search Across Site collections and Web applications, People search, Metadata property search,keywords, synonyms, and Best Bets.

Metadata properties for search in Microsoft SharePoint Server 2010. When content is crawled, the crawler also crawls the metadata that is associated with that content — for example, information such as author, title, and e-mail address. The search system stores this information as crawled properties and managed properties. Crawled properties are all properties (such as author, title, or subject) that are extracted from documents during crawls. Managed properties are crawled properties that can appear in refined or advanced searches. When users perform a general search, results include items with any crawled properties. In order to provide refined search capabilities to users, however, you need to plan for managed properties. Because they can appear in refined searches, managed properties help users perform queries that are more successful and relevant. SharePoint Server 2010 provides a default set of managed properties, but you can create new managed properties and map crawled properties to the managed properties that will appear in search result. Refined searches can be performed only on managed properties, not crawled properties.
The properties that are automatically created include the following:
Author, Description, Site Name, Type, File Size, Last Modified Date, URL, Title

Reducing duplicate managed properties:
crawled properties might be Owner, Writer, and Created By, all of which are synonymous with Author.  plan to create one set of managed properties and map the crawled properties that have the same meaning to managed properties. In this case, you map Owner, Writer, and Created By to the managed property Author.
Managed properties scenario:
Example a customer service representative identifier (ID) property in a separate data application, or an Author property for an application type that is used exclusively by customer service representatives. A search query that uses that property or a term associated with that property will include search results for all items that contain any of the crawled properties mapped to the customer service representative ID managed property.

Keywords, synonyms, and Best Bets:
Keywords are search terms that users type into a search box when constructing a query. Users can use them in queries that they submit in the search box on a site, on the Search Center, or in an Advanced Search. When a user query includes a keyword that you have configured, the search results can provide a definition for the term together with links to recommended locations or documents at the top of the search results page.You can define keywords, provide synonyms (words that closely relate to the keyword), and create Best Bets (links to featured documents or locations for the specified keyword), to provide a relevant set of search results for popular search terms. Synonyms are useful when several search terms are used for the same concept and content so that search results are merged and not scattered across several search terms. When you create a keyword, you can also provide a definition of the keyword that appears in search results. By defining terms that are often used in searches as keywords, a site collection administrator can provide a standard glossary of names, processes, and concepts that are part of the common knowledge shared by members of an organization.
If you already have search set up in your production or test environment, you can use Site Collection Web Analytics Reports to help you plan keywords, synonyms, and Best Bets. The reports that are most useful for this effort include the following:
Top Queries, to view the most common search terms.
No Results Queries, to view the most common search terms that yielded no search results.
Best Bet Usage, to view the most frequently-used Best Bets.
Best Bet Suggestions, to view the suggestions for new Best Bets that the search system provides.