What are the differences between creating Search center as a subsite vs a new site collection? What are the benefits of creating it as as new site collection v.s a subsite.
Applies to both Enterprise and Basic Search Centers:
Search Centers should be separate site collections because they search for information across a company portal or division. If you create a Search Center as a sub-site, you might have to create some workarounds for a full customization.
Personally, choosing site collection over subsite will definitely provide you performance, simple url (managed path complexity) and greater freedom to manage and scale the service down the road, whereas sub-sites are generally more limiting.
Here is reference: http://technet.microsoft.com/en-us/library/cc262410.aspx