SmallSearchInputBox does not seem to show the same query suggestions(global query suggestions manually added through central admin are shown) as the search box in the search center. Furthermore, it shows different suggestions at the root site and at the sub-sites. Users end up seeing different query suggestions at different levels of the site hierarchy. I knew query suggestions were aggregated at result source and site-collections levels. But this behavior seems to suggest that query suggestions are stored at individual site level.
Also tried to use the SearchBoxScriptWebPart instead of the delegate control and different settings but that did not help either.