In a stove top coffee maker the water is boiled in the lower chamber, the steam pushes the water at low pressure upwards through the grounds before reaching the upper chamber, let's call it decanter. So the water is in contact with the grounds only once. Due to the high temperature there is arguably over extraction happening. In terms of flavor you can tell by the slightly bitter taste. Another factor contributing to this is that the fines are flushed out with the water, ending up in the decanter and your cup where they keep extracting bitter compounds. This can be minimized using some tweaks, but it's not preventable.
A percolator in comparison keeps circulating the water and brewed coffee through the grounds, reaching an even higher extraction ratio. The water and continuously the brewed coffee is heated, pushed upwards and "dropped" on the grounds before it sinks down towards the heat source again.
The difference in taste stems from the rules of extraction. The first substances to be extracted are caffein and acids. Caffein is bitter, but adds only partly to the bitterness in coffee compared to other compounds extracted later. The acids give coffee fruitiness, which is usually a desired quality and forms the base of the taste profile. The bitter compounds and sugars are extracted last. You want mainly the sugars in your cup to add sweetness, the bitter compounds you want to avoid. They make the coffee taste hollow, ashy, a bit like charcoal or burned rubber and leaves you with a kind of empty feeling after swallowing it. By that I mean it has no pleasant lingering after taste.
So basically that is what's happening with percolators. They over extract, meaning too many of the bitter compounds get in your coffee, which makes it unbalanced and just overall not really tasty. I would say it's probably one of the worst methods out there to make coffee nowadays in terms of extraction. There is of course a subjective component to it. Some people might enjoy exactly this taste. Maybe they want that burned taste, then add lots of sugar, milk and/or flavors and that's just what they like. That's of course ok, but the facts remain, that you lose complexity, fruitiness and sweetness.