I am looking for an SWT widget that would have the look and behavior similar to Swing's JPlitPane. Is there such a widget in SWT, and if not, what's the closest to it? (A pane split to two with the ability to move the border between the two parts)
Take a look at the SashForm:
From the javadoc...
The SashForm is a composite control that lays out its children in a row or column arrangement (as specified by the orientation) and places a Sash between each child. One child may be maximized to occupy the entire size of the SashForm. The relative sizes of the children may be specified using weights.