The clue to most portrait lighting can be found in the eyes!
Look at the picture of the man, large catchlight in the eye plus a couple of smaller catchlights, now look at the catchlight in your eye, small spot.
I would suggest the man has been lit by a large strong lightsource which is mainly hitting him from his slightly front left, this is probably from an open door or large window, this gives a degree of additional light spilling onto his right cheek which although not as strong (due to fall-off) gives added depth and definition. I suspect the other catchlights are from additional windows in the room.
Now a self portrait whilst fun is not the best way to learn how to use lighting for dramatic effect. Neither is a stobe to be honest. It is much better to learn with available light and use reflectors and flags to control and direct the light before moving on to strobes and speedlights.
In your self portrait, whilst you have tried for dramatic lighting, the light source is too far to your right which does not allow the spill of light across your face to give depth and definition, it is also pretty much on the same plane, so the fall off is not so pronounced and therefore the contrast is not as high on the lit side of your face as the light on the old mans.
If you want to learn how to light different portraits, I would get yourself a model ( male is probably better than a female, they won't be so upset with some of your failed attempts), try to find a room with a large window (preferably with dark walls) get a couple of white reflectors (card will do) and a few bits of black card (for flags) and then practise at adjusting the light by moving the subjects position, controlling and moving the shadows with flags and reflectors and seeing what happens with the use of different camera positions relative to the light source and models position. Once you understand how to use available light, then, and only then, should you try the same thing with flash units (either studio or speedlights). this will be much more difficult as you have to actually take an image to see how the effect has come out.
Good luck and remember, good practise will improve your understanding and skills.