piston/head design vs. HP question

Would there be a difference in HP (all else being the same from set-up to set-up) between a
piston with a dome/large CC head and a flat top piston with a small chamber head? Guess one thing right away might change and that would be ignition advance. If the heads flowed the same, compression and rocker arm ratios the same, camshaft the same,would there be a noticeable difference? Thanks! Bob