I'd use water channels to funnel both into the same drop of about 20 blocks so I can kill both at once (yay for sweeping strike of swords.)
They will not inhibit each other - this kind of spawner ignores the mob cap.
The more difficult part for me would be researching what kind of elevator could lift these mobs in order to get them to an elevation to drop 20 blocks while I am still within 16 blocks of each.
Water elevators have changed their operation in recent updates. Think a bit about how you want to treat baby zombies too. One tip - baby zombies cannot fit under a trapdoor, so fit the opening of your kill chamber with a trap door.