Creating a custom model via the model manager is an extremely restricted way of creating a model. The tools is a minimal viable product and as such only provides access to maybe 60-70% of the features. It also adds various issues around model lifecycle management and potential reuse. The Content Model Manager in Share was implemented as an after-thought to support prototyping / trivial customization use cases.
In my point of view, there is only one way to define custom models, and the Content Model Manager is "just" a tool that allows non-technical people to create trivial models with a limited scope (and still shoot themselves in the foot) without having to understand much of the underlying technical impications.
Since the Content Model Manager creates a model just as if that model would have been defined in XML, there are no differences with regards to features that work on nodes using types / aspects / properties from that model. Search works just the same....
