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:
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