P31 Controller described a near loss of separation event; noting that the current automation fails to display needed information at the correct position/display.

Narrative

While working the A-AR; I accepted a handoff on aircraft Y; 24;000 FT southbound over NSE arriving NPA as per LOA. I then observed Air Carrier X; 15 south of CEW westbound at 24;000 FT; converging with aircraft Y. As soon as aircraft Y checked on I descended him without delay to 22;000 FT to avoid this conflict. As I was doing so; ZJX was calling me to inform me of the conflict and I told them what I was doing about it. The problem here is that aircraft on flight plans that will over-fly us from 24;000 FT or higher automate with the E-AR; even though the E-AR has no airspace above 16;000 FT. When I observed Air Carrier X; it was a limited data block and was displayed on and automating with the E-AR; but was anticipated to enter the A-AR airspace if descended further. It could have gone completely unnoticed! Recommendation; change the automation so high altitude over-flights will automate with the A-AR and the correct positions will have a full data block with more time to plan and execute separation.