M03 controller described potential conflict event with two departures being transferred to ZME with an overtake situation developing; reporter noting differing RADAR equipment types may display different speeds.

Narrative

I was working East departure and arrival combined. Aircraft X departed eastbound on the MEM 7 departure followed by Aircraft Y. As each aircraft approached 10;000 in the climb; I asked each their airspeed above that altitude. Both answered 290 knots. Memphis Center (ZME) took the hand-off on Aircraft X; and I switched him to their frequency. As Aircraft Y climbed through 14;000; still indicating 10 knots slower than Aircraft X ahead; I called ZME and told them that both aircraft advised a speed request of 290 knots. ZME replied that Aircraft Y was indicating 15 knots faster; but he would still take the hand-off. I said that my scope showed Aircraft X going ten knots faster. ZME replied that now Aircraft Y was indicating 35 knots faster while my display showed the aircraft at like speeds. After the situation; another controller at my facility said that there was a spot east of Memphis that would give ZME a false overtake read-out because aircraft were transitioning from one radar feed to another. I have no way of knowing when ZME will see this false overtake; so I assume that I am giving them a clean situation that needs no coordination.