"A beautiful woman always draws my attention".
"While I was chatting at Laura's party, a beautiful guy suddenly drew my attention".
«Now I wish to draw your attention to what has attracted my attention most». (Enigmas of Psychical Research)
But can I say, e.g., "my research in social psychology has drawn my attention to the relevance of theoretical physics for behavioral sciences"?
What it should be conveyed in the last phrase is the idea that you were doing something – studying social psychology – and that brought you to do something else which, externally, seemed quite different from the first activity. The attention, as it were, strayed from the first topic to the second one and that was due to the first topic's inner feature. I would not conceive 'attract the attention' as a valid alternative, for it lacks that compelling and coercive element 'draw' seems to imply.