I do exactly what you describe - my laptop has a trackpoint and a trackpad, and I use the former because I find it more precise. However, trying to chase moving objects is very frustrating, and dragging isn't that great either.
It's been a while since I last had one, and I don't remember trying to play with it...
I used to find it completely unusable until I finally discovered the proper way to use it (probably when I started to touch type) which was quite an epiphany. I wanted to share just in case you hadn't yet discovered it.
The big difference for me was turning on pointer acceleration and pushing the sensitivity way up, to the point where just placing a finger on the stick starts the pointer moving. That way you're not actually using very much pressure, and it makes using the stick much more comfortable and intuitive.
Having a decent cap on the thing also helps: my first TrackPoint (about ten years ago) was on a third-hand laptop, and the rubber had decayed to the point where it was squishy and sticky. Not very pleasant to use :)
The clit mouse is designed to be used by touch typists. You don't have to leave the home row to use it (use your thumbs to click).
If you handle it with the index while the other fingers of that hand rest on the keyboard (so that your hand is fixed), it becomes very precise.