You'd have to have advantages and disadvantages to being a person / zombie.
I'd suggest something along the lines of:
"The Living" (I'll call it for simplicity): two modes of moving, one slightly slower than the "The Dead's" default walk, another, a sprint. The Living has a fatigue meter, and when "sprinting" that fatigue meter fills up. After certain points a person will trip and fall when running. Every trip / fall there is a some injury, and when health is below a certain point, The Living becomes unable to run for a long period of time. The Living can cross certain obstacles that The Dead cannot without breaking or moving. The Living will also have access to some weapons to fend off The Dead on open ground, and can create barricades. Barricades are created very slowly, however, and other than a simple door block you'll need a team of people to build a decent barricade. The Living also rely on food, so they can maintain their health.
The Dead, however have some powerful options, but are unable to sprint. This means that they can easily surround an injured Living that does not have any weapons or has run out of ammo. Rather than a health meter and fatigue meter, The Dead has a stun meter and frenzy meter. Weapons will stun The Dead, but only a little unless repeatedly attacked, to which point the afflicted Dead is unable to move temporarily. However, when a group of The Dead get together, their Frenzy meter builds up, and they can go into Frenzy mode. The higher the frenzy meter, the more damage they do to The Living and barricades, and the less stun damage they take. A good mob of The Dead can plow through barricades fairly easily, so The Living will have to relocate often, relying on their sprint and limited resource weapons to get away.
I have a couple more ideas, PM me if you'd like.