Are you looking for a real estate website with IDX, or an IDX feed to put on a website?
With a website complete with IDX, you can better track customers and follow their leads and activity through your lead management system and seamlessly use e-Marketing tools (drip marketing, eCards, etc) if your website offers that technology.
If you have an IDX feed on a current site, it may offer lead notification, but probably is lighter on the lead management and e-Marketing side.
If you frame a property search from your website, you can display all listings, but lose all lead management capabilities. Typically, in this case, a consumer will have to directly E-mail you for questions or showing requests.