TransactionScope relies on the ability of the ADO.NET provider to bump up the transaction to a distributed transaction if there are multiple connections, which relies on MS DTS and that's not implemented in the .NET core version of SqlClient. You might not run into this, but as it's a limitation we recommend to use the net fx version for net fx.
the differences between the builds for netstandard and netfx are minimal, they're mostly around config file usage and binary serialization, as well as type discovery for DI, which uses an appdomain on netfx and that's not possible on netstandard.
If you use RuntimeConfiguration to configure your application, including specifying which DI types you might use, avoid binary serialization, the transition should be smooth.
*edit heh 5 seconds apart