Fast zombies as depicted in 28 days later. Technically, not dead, just infected with a virus that make them go crazy and run around looking to kill as many people as possible. You could kill them like normal people. Starvation, let them bleed out from injuries etc.
Slow zombies as depicted in all kinds of zombie movies. Only killing their brains will stop them from trying to eat you.
I think fast zombies are scarier. Even if you could kill them like regular people, that is still more threatening than having some slow zombies creep up on you.
For instance, with slow zombies I would feel comfortable getting a knife or whatever and stabbing them. They are slow enough I could probably deal with it. Even if there are multiple, you could weed them out slowly. And, if they ever get too close for your comfort, you could run away and get some distance on them. However, with fast zombies, there is a good chance your knife will only prove effective against maybe one or two. Even that would be risking it because they'd be harder to hit I feel. (Stabbing them in the stomach or whatnot won't kill them immediately). And, if these ones ever get too close for comfort, you could try to run but chances are they'll be running the same speed as you. You're kind of screwed in a pack.
People could set up extermination squads and get rid of slow zombies relatively easily. Fast zombies would most likely kill the majority of people pretty fast before the zombies could possibly starve out or whatnot.
Logically speaking slow zombies wouldn't be that hard to deal with. Ignoring the fact that flesh deteriorates incredibly fast after death they would still be easy to round up. Just put speakers in a cage and when it's full set them all on fire
Fast Zombies are terrifying. I freak out enough just when a regular person like my brother or my boyfriend chases me let alone a zombie. Just the idea of someone running behind me starts to freak me out and I scream a lot. xD