When a framework matures to a certain point usually its a good idea to start again. This might sound counter productive but its a good chance to learn from the mistakes you made the first time and to create something without legacy code that may not be needed.
For awhile this has been the goal for the new .net frameworks with libraries becoming increasingly modular so especially on servers, you only used what you needed.
In an attempt to go a step further, asp.net and .net have forked off and created the core 1.0 frameworks which have been developed from scratch. Both 4.6 versions will still be available and maintained while the core framework matures into something that is production ready.
To be clear, ASP.NET 4.6 is the more mature platform. It's battle-tested and released and available today. ASP.NET Core 1.0 is a 1.0 release that includes Web API and MVC but doesn't yet have SignalR or Web Pages. It doesn't yet support VB or F#. It will have these subsystems some day but not today.