I think this may be wrong question to ask! Rather than choosing a scale that is likely to produce significant results, what is more important is to choose the scale that is appropriate for answering the intended question. That, not the significance, should be the criteria to choose the scale. 

I think this may be wrong question to ask! Rather than choosing a scale that is likely to produce significant results, what is more important is to choose the scale that is appropriate for answering the intended question. That, not the significance, should be the criteria to choose the scale. 

You are taking a continuous variable and turning it into a categorical variable. There are at least two effects. 1) If a person's perception is incapable of fine scale quantification then having too many categories generates noise. On a scale of 1 to 100, how are you feeling today? Why did you choose 74 and not 73, are you that much happier? A 100 point scale doesn't work very well here because it is too fine relative to my ability to choose 73 versus 74. The same phenomena applies in choosing a 5 or a 7 point scale: can you separate a 20 percentage pint difference, or are people a little better and capable of 7 or even a 10 point scale? 2) There is an issue of how the scale interacts with the distribution of answers. Choosing the wrong scale could hide or exaggerate the true answer. Maybe in one scale the true population mean lies at the midpoint of one of the intervals, yet in the other scale the population mean lies at the boundary between two intervals. Your choice influences your results. Try generating a bunch of random numbers from the normal distribution. Generate several histograms with different numbers of intervals. See how that influences your perception. 

. Timothy Ebert has already made his point clear. I will provided my summary of observations on Likert scale.   I hope it will answer to a extent your question. 

The studies  have found that the five and seven-point scales may  produced the comparable mean scores once rescaled. 

it appears that indicators of customer sentiment – such as satisfaction surveys – may be partially dependent on the choice of scale format.

Compare to 5 or 7 point scale, a 0-10 point scale may produce better results. Where 0 indicate totally no agreement and 10 point indicate complete agreement. 

I don't believe one can give a general answer to your question. It will strongly depend on what kind of tests you want to do. Do you want to do a comparison between two groups answering the same question (Mann-Whitney U test), do you want to corelate two such items (e. g. Kendall correlation), do you want to use items in a multiple regression? Also it will depend on which is the "true" distribution of the underlying theoretically continious concept.

For choosing answer formats there are many options, and as the previous answers pointed out, there are different reasons to choose one or another option.

The first question would be, is a Likert scale really the best scale? 

Who will answer the questions- if you have children or less well educated persons dont choose many points for the scale.

What calculation do you want to do? If you want to use individual item scores as continious variables e.g. in regression analysis five-points will be to less, seven might already be appropriate. And so on.

The KEY question is what scale to use. And that, as I suggested earlier, needs to be primarily decided not by statistical significance considerations but by the intended subject-matter objectives, the context, and the background of the responding subjects (=study units). Consideration of these criteria will help choose a scale which is more likely to reflect the truth. All else should follow from that - including which statistical methods are appropriate to use. 

A five-point scale might work better for some respondents because it makes their choices a bit simpler:  a 1 (unsatisfied) or a 2 (somewhat unsatisfied), or 3 if completely neutral.  A 7-point scale is a little harder for some people to make choices, although the center value (4) is still neutral and this is visually obvious on the printed scale.  If your scale has too many numbers and choices, then some people will have difficulty deciding and "somewhat unsatisfied" could legitimately be either a 2 or a 3.   It may help to  have corresponding words with each number, such as "somewhat satisfied", "mostly satisfied", etc.  to help respondents get a feel for the meaning of the scale.   With a 7-point (or 10-point) scale I would think you would have more opportunity to see a one-point difference in scores as becoming statistically significant.  But some respondents will see those fine differences as meaningful increments of how they feel about the answer and some won't, so a "significant" difference might not accurately reflect the true feelings of your study population.  You can get more precision but you'll have more noise with a 7-point scale.       

We recommend using 7 point Likert scales because they balance choice against working memory modelling: if you use more than 7 points then it is hard to discriminate between individual options (in a new field) and you tend to get a left - middle - right distribution; if you use less than 7 points then you are reducing the richness of the data.

If you only anchor the end values of the scale with interpretations then you can treat the data type as scale rather than ordinal, which means you can calculate means and standard deviations, for example.

Another important idea to keep in mind id that a Likert style scale needs to be as sensitive and accurate as possible.  From this point of view a 7 point scale is more sensitive as it gives the participant more choices to indicate the strength of their response.   Thus a stronger scale.  An even more sensitive scale would be one drawn with a ruler X centimeters long (X must be an odd number as a scale needs a center point that indicates neutrality). Furthermore each millimeter is also marked.  This type of scale gives the participant a chance to indicate their preference at the millimeter level thus increasing the sensitivity and accuracy of the scale.  While this is a tedious process in a pencil and paper environment I have seen it used vary effectively in a computerized environment.