What is the difference between BasicHttpsBinding and WsHttpBinding with Transport security?

As BasicHttpsBinding is new at .net 4.5, I don't seem to be able to find much stuff around differences between the two.

Indeed the two bindings are very similar. The only real difference is that to require HTTPS, the endpoint needed to be configured with a BasicHttpBinding in which you define the security mode as Transport (or any of the other valid enumerations). With a BasicHttpsBinding on the endpoint, the security mode is defaulted to Transport and the client credential type is set to None.

So here was your configuration before WCF 4.5:

<system.serviceModel>
  <bindings>
    <basicHttpBinding>
      <binding name="Service.BasicHttp.BindingConfig">
        <security mode="Transport" />        
      </binding>
    </basicHttpBinding>
  </bindings>
  <services>
    <service name="ServiceImpl">
      <endpoint address="" binding="basicHttpBinding" bindingConfiguration="Service.BasicHttp.BindingConfig"
                name="IService.Http" contract="IService">
      </endpoint>
    </service>
  </services>
</system.serviceModel>

With WCF 4.5, the same configuration can be simplified to:

<system.serviceModel>
  <services>
    <service name="ServiceImpl">
      <endpoint address="" binding="basicHttpsBinding" name="IService.Http" contract="IService">
  </endpoint>
</service>
  </services>
</system.serviceModel>

See What’s new in WCF 4.5? BasicHttpsBinding for additional detail.