.NET Core is faster than .NET Framework

One can hardly call .NET Core "a library." It's an API surface area (.NET Standard), a cross-platform implementation of said surface area (.NET Core), a cross-platform runtime (CoreCLR), and a CLI tool (dotnet). It's already introduced numerous performance enhancements over .NET Framework (e.g., Span<T>, Memory<T>, and the runtime itself).

IMO, .NET Framework should be relegated to the dustbin of history. There is no longer a reason to use it unless you are writing legacy code (which, granted, is a legitimate reason in many cases). For greenfield projects, I hope you're using .NET Standard and .NET Core.