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. For example, sub-sites all exist in the same site collection container and if two sub-sites grow beyond a manageable size for a single site collection, that container cannot scale out its storage without breaking the collection apart into several site collections and facing other challenges (like changing URLs or having managed path complexity, and data migration efforts).
Here is reference: http://technet.microsoft.com/en-us/library/cc262410.aspx