This is a hard question to answer. I initially didn't 100% agree with the idea that there are tricks that are inherently stronger than another and I do still think that a good presentation can elevate any trick. At the same time, there's a reason we say people can "buy their powers" in magic. I have seen some really bad performances of great tricks (Double Cross, Invisible Deck, and Omni Deck come to mind) that still seemed to fry people.
However, I've also seen great performances of lame tricks (Bill Malone's 21 card trick) that worked really well and some really terrible performances of those great tricks that did not seem to hit the audience the way it should have. So I'm still not really sure if I agree with the idea that there are tricks that are inherently more powerful, but I definitely see where you're coming from.
My first instinct would be to say is that tricks that maximize the "cognitive dissonance" between what they know to be true and what they just saw tend to be more "inherently" strong. I think this could be why a lot of card magic doesn't have a lasting impact for people. They don't know exactly what you did, but knowing that you did something is enough of an explanation for them. There are tricks where it's not as easy to jump to this "non-explanation". Going back to Double Cross, they "know" you didn't touch them and they also "know" that there's no way you could have used sleight of hand to draw a perfect X on their hand. Yet it happened and they have no way to explain it away. The thing is, there are ways to elevate most tricks to this point. Some really minor changes are often all it takes such as doing it in their hands instead of your own.
Obviously having a deceptive method is important. If they can figure it out easily, it won't be as strong. But at the same time, there are plenty of tricks with fooling methods that aren't that interesting on their own. Tons of magician fooler card tricks seem to be this way. Sure the method is nearly bulletproof, but at the end of the day it's just a "was this your card?" trick with a ton of extra steps.
Part of it is also surprise. Joshua Jay did a survey and the most common answer for "what do you like about magic?" was "surprise". Don't quote me on this but I remember reading that on a brain scan, a person's reaction to a magic trick activates the same regions of the brain that the punchline to a joke does. People like to be surprised. Of course, surprise is a very short lived reaction and there are plenty of tricks out there that get a short term "surprise" but don't have any lasting impact. As stated before, a lot of card magic has an initial surprise, but no lasting impact. It could be related to people being able to fall into the non-explanation of "sleight of hand" but I'm not sure. It's just me speculating.
As WitchDoc said, having a presentation that connects with your audience in some form is very important in having a powerful trick.
So in the end, I really don't know. This kind of reminds me of the age old question as to whether the presentation or method is more important to a magic trick. My take on that debate it's a combination of both but for different reasons. I think it's the same thing here. It's a mix of factors that can vary between the tricks themselves, the person performing it, and even audiences. A person who likes to gamble might find a gambling demonstration much more impactful than someone with little knowledge of poker. As I said before, a trick that fools magicians might not be that interesting to most people.