Minitek Live Search is more suitable for a small to medium number of articles. It has more data source parameters, allowing you to specify the data source with great detail. It does not use an index therefore search is slower and not very intelligent. It only supports Joomla Articles, K2 Articles, Jomsocial content and Virtuemart Products.
Minitek Smart Search is much better for a medium to large number of articles. It does not have as many data source parameters as Live Search does, but it scans the content of your website and builds an index that enables fast and intelligent searching. It also supports any 3rd party Joomla component that includes smart search plugins.