Hi Xavier
The projection in OSM and Google is the same. Coordinates are equial.
Today I started development import from Google and Yandex extensions.
You can see Utilities tab in OpenStreetMap extension.
Today I only inport groups, but in a few weeks - all of data.
I step by step include featues, which are in Google's extension.
As for hovering - I decided how I will do it, and in a few days the new release will be with this feature.
Today I still not implement AJAX loadin infowin content, AJAX loading map objects, infobubble (tabs in infowin), cluster icon overriding, detail view of placemark, user entering placemarks and so on.
As you can see - this options you can enable. But I'm thinking of it and when have time - implement and do releases.
It's too hard to implement all features with short free time. But I'm trying.
As for styling. I think you should check different map types.
For example this is some demos
leaflet-extras.github.io/leaflet-providers/preview/