I think the difficulty in this is getting a lot of information represented in such a small icon without needing to make it too large and distracting. Showing who owns the point, where the point stands in the 'tug of war', how many ships are on the point, if it's converting, etc.
The inside symbols probably aren't needed, as the ship counter and ring around the circle let players know who owns it, and if it's being contested/blocked. Although they do make it look a lot more interesting than just the ring. Right now the ring turns blue when blue owns, red when red owns, and white when it's neutral.
Although that'd really just bring us back to square one, but instead of a ship count number being displayed, it'd just use the wedges.
If I had to pick, I think Djinn's design is more visually appealing than the current system as well as more effective.