The latest ASP.NET released version is ASP.NET 4.6.1 and we are waiting the ASP.NET 5 (Core) to be resealed, as there is candidate release already. So, to in this terms to use the ASP.NET Core hosting you should have a VPS or dedicated server, and to use ASP.NET 4.6 you should have shared, VPS, or dedicated server. Bellow you will find the new features in ASP.NET 5 hosting and the new features in ASP.NET 4.6 hosting.
ASP.NET 5 hosting
– Ability to host on IIS or self-host in your own process
– Built on .NET Core, which supports true side-by-side app versioning
– Ships entirely as NuGet packages
– Single aligned web stack for Web UI and Web APIs
– Cloud-ready environment-based configuration
– Build and run cross-platform ASP.NET apps on Windows, Mac and Linux
– Open source and community focused
ASP.NET 4.6 Hosting
– Cryptography: Support for X509 certificates containing ECDSA;
– ADO.NET improvements as always Encrypted support for hardware protected keys and improve MultiSubnetFailover connection behavior for AlwaysOn;
– Windows Presentation Foundation includes a number of improvements and changes as improved performance, spell checking improvements and additional support for per-user custom dictionaries;
– Windows Workflow Foundation: Transactions. The Transaction.EnlistPromotableSinglePhase method can now use a distributed transaction manager other than MSDTC to promote the transaction.
– Native Image Generator (NGEN) PDBs. With Ngen PDBs, NGen can create a PDB that contains the IL-to-native mapping without a dependency on the IL PDB.