Performance benchmarks have also been exciting: https://github.com/aspnet/benchmarks
I am working on samples for aspnetcore here https://github.com/dodyg/practical-aspnetcore
Boilerplate code sucks, but there are ways to minimize it, and when something breaks you can follow the path through your code to see why.. you don't have to try to discern the interaction between the framework code, your code, defaults/convention and values you do have configured.
The MVC pattern is the same and you will be learning C# and Razor for both. The differences are in the details but many of the skills will be transferable. For example, the way bundling and minification are done is now different (built-in before and now JavaScript runners like gulp).
Shameless plug; I cover these difference in my book "ASP.NET Core 1.0 High Performance": https://unop.uk/book
On the enterprise space, .NET Core is still quite irrelevant.
Our customers are slowly migrating from .NET 4.0 to .NET 4.5 (not even 4.5.2!), let alone .NET 4.6 or .NET Core.
If you're learning for the fun of it, it really doesn't matter, but 99% of work being done in ASP.NET is on the existing .NET stack (MVC/WebForms). It's not a corporate thing, or an enterprise thing. We use .NET because it's a mature platform, and ASP.NET MVC works. I work in an agency on MVC builds, and I doubt we'll be using .NET Core for at least a few years.
If you know one, you can easily move to the other
Any new project I make will be using Core. It is the direction .net is headed.
Regular = MVC/WebAPI
Classic/Old/Shit = Webforms
It either case it comes down to discipline.