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In OpenLayers 2, clicking a geometry with an active modify control running, created a drag vertice on every edge of the geometry which could be used to modify the geometry by dragging.
In OpenLayers 3+ with the modify interaction, things are different. Clicking a geometry instantly activates one vertice only that can be dragged.
Can I obtain the ol2 behaviour in ol3+ as well?
It can be imitated. You woould need to use a custom style to style the vertices and midpoints similar to https://openlayers.org/en/v4.6.5/examples/polygon-styles.html then use a custom condition function which checks proximity to those points.
The OpenLayers 2 example http://dev.openlayers.org/examples/modify-feature.html
The standard OpenLayers 4 example https://openlayers.org/en/v4.6.5/examples/snap.html
A custom version of the OpenLayers 4 example https://codepen.io/mike-000/pen/NWKvLdG
