If the zombies you are dealing with are, in fact, reanimated corpses, in all likelihood they will be slow, because, as you say, they are decaying corpses. Although, the very recently dead may retain more mobility since their bodies are more "fresh".

This, of course, accounts for scientific reanimation of dead tissue. If instead we are dealing with a virus which reduces the cognitive abilities of the subject to animal levels and base desires of hunger, or some form of mystical enchantment, well, all bets are off.

In the event of a zombie outbreak, it is very important to quickly identify two things. First, which type of zombie you are dealing with, reanimated dead, parasite infested, television brain rot, voodoo, and assess their capabilities. Preferably, from a distance or through an otherwise impassible barrier. After understanding the capabilities of the zombies and securing yourself from them, the next thing to identify is if there is an immediate cure for whatever is happening. If those affected can be "snapped out of it" you should make attempts to do, though never at risk to your own life.

The last part of that last statement is key. Whether fast or slow, as a non-zombie your life is more important than that of a zombie, even if they can be cured. Much like on airplanes where they tell you to secure your own oxygen mask before assisting others, you can't help anyone if you are a zombie, so when in danger aim for the head.