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Which of the following two sentences is more correct?
OR
Nothing important, just my own quotes! Do also suggest, if I can put it in a better way to express what I want to.
I feel: "A picture says a thousand words, more importantly in a fraction of a second"
sounds better.
Here, 'better' implies that even though it is an important attribute of a picture that it says a thousand words, what is more important (which makes it even more effective) than this is the fact that it does so really quick i.e. in a fraction of a second! So, you compare 2 things and say which one is better. One should have at least 3 things, to state which one of them is the best. You could capture the same emphasis if you had said: "A picture says a thousand words, and does so in a blink of an eye!"
PS. Not all pictures can say a thousand words, even among those that do, not all can actually do it in a fraction of a second. After all, a picture is not just what is been shown, it is really what is been seen. The picture owes many of its attributes to the beholder.
It depends what you want to express.
"Most importantly" can mean one of two things:
Since your sentence doesn't provide a number of options, the sentence conveys the second meaning.
"More importantly" means "of these two things, this is the more important one". It's difficult to find the thing you're comparing to, but I suppose it's that the picture says a thousand words. So that sentence indicates that the speed with which a picture conveys information is more important than the number of words it conveys.
Neither sentence is particularly elegant. I suggest:
A picture says a thousand words - importantly, in a fraction of a second.
Also note that the familiar phrase is "A picture is worth a thousand words."
RE "better way to express it":
First, as Karthik says, the conventional phrase is, "A picture is WORTH a thousand words." But if you use the standard phrase, it's difficult to see how you could add "in a fraction of a second". "Worth" doesn't "happen" like "says" does.
To go back to using "says" for a moment: While your meaning is apparent, your examples are awkward. You have two adverbial phrases, "most importantly" and "in a fraction of a second", stuck together, which makes the connection to the object or objects obscure. Phrases like "most importantly" are routinely used with no object, but combining it with "in a fraction of a second" gets clumsy. You could say, "A picture says a thousand words in a fraction of a second". Note there shouldn't be a comma in there. But it's not clear where to add "most importantly" without gumming it all up.
I suppose the grammatically correct way to say it would be, "A picture says a thousand words, and the most important fact is that it says them in a fraction of a second." But that's not very catchy. My inclination would be to write, "A picture says a thousand words, and most importantly, it says them in a fraction of a second." Then "most importantly" has no object but you get away with that, and "in a fraction of a second" clearly modifies the second "says".
Now if you substitute the "correct" phrasing, "worth", the sentence works: "A picture is worth a thousand words, and most importantly, it says them in a fraction of a second."
