Which style of bidder selection is best?  That really depends on context.  
 
For private companies involved in repeat execution of similar projects in similar markets, a single-phase invited bidders list makes sense in that research into contractors is an ongoing activity with new companies being invited and evaluated for less sensitive or smaller projects.  
 
For public bodies, typically a two phase prequalification/bid process works best for the following reasons: being involved in fewer projects that are unique, or one of a kind makes for less current market knowledge that may not be transferable to other projects; a requirement to procure projects either with prequalification for an invited list, or call open bids (being mindful that the latter may well require considerable post-bid evaluation effort).
 
The following provides an illustrated comparison of the single stage, two stage, or hybrid Construction Procurement processes with these Bid Types.