No right or wrong answer exists for this one. I think the best way for us to give you any advice is for you to shoot a video of yourself performing it with the different patters.
In the end, when you have performed enough, you will find out which patter works the best for YOU. Remember, your audience's perception is completely subjective. Some may like the story style, some will prefer "to the point." Any patter is good (in my opinion) as long as the effect is clear.
I think it was Dai Vernon that said the effect should be able to be described in one sentence. As long as your spectator can do that and is not confused by what happened, then your performance of the effect has succeeded. The story is where you want to tug at their emotional heartstrings and is what will have the most impact.
So in short, try to rehearse both as much as needed. The story is definitely important so it would be good to write out your patter, test it out on friends, revise the script, and test it out again. For the effect, make sure it looks clean and you don't flash anything. Once you have those two things down I think you should be good.
If those are the two options you have, go on with telling the story. Because it doesn't make sense to explain the effect, although many magicians do that and they come off as looking very...well, let's just say that it looks very weird.
I mean, they can see you put it in. So why do you need to say that you put it in?
I mean doing it once or twice IS OKAY. But doing it throughout the trick will definitely make the audience question if you had too much of tetrahydrocannabinol.
But jokes apart...it doesn't look or seem good.
So that's why my vote goes to the story. But isn't it often better to let the magic do the talking for the maximum impact?
Well, for example I do this trick where the card turns itself in a deck. And I use a very 'psychological patter' for it. However, in the past I would say "You imagined the card to turn over in the deck" and this line, which should be said once or twice, I would say a million of times. Though the reactions on the climax were still great, I got a lot more better response when I said the above line only once.
Because believe me, when the audience reconstructs your performance, they will not ignore that vital piece of information like they had just imagined the card turn over (an example) even though you said it only once.
My advice is that unless the performance needs you to be really vocal, let your magic speak and keep words to a minimal.
PS:- I DO NOT PROMOTE THE USE OF TETRAHYDROCANNABINOL.
I would say that what you say, if anything, depends on the particular trick or routine - and your personality.
Good advice in magic, and in life in general: Be yourself.
Explanatory patter, such, as "Now I m going to..." or "All I have to do is wave my hand like this..." is not entertaining, and may insult the intelligence of the spectator. Most often it is outright boring.
Stories may go very well with some tricks, and people like stories if they are interesting, intriguing or funny and fit what you are doing. But if you're going to tell a story, make it a short story, not a novel. And sometimes it might be preferable to be straightforward and mysterious, or say little or nothing. Whatever your patter or story is, it should not be long and drawn out. (Think about those people who draw out a joke or recount a story that seems like it goes on forever until you are practically praying for it to end.)
For me, a lot of the fun in magic is the creativity. Experiment with different scripts and patter, and you may end up changing or improving how you present something. The reactions of your audience are the best guide to telling you what works. I like to involve the people and make them the center of attention. After all, in any performance art, it's about them.