It depends on choke & barrel length - your needs seem at odds with themselves, as Patridge hunting is usually a close-range, open choke affair (in my experiences) usually with a short-barreled gun; and Trap shooting usually involves a long-barreled, full or modified choked gun to reliably track & break clay pigeons.
Patridge hunting and Skeet or Target Clays shooting are most compatible with each other - both for conditions & equipment.