There is a close relationship between Euclidean distance and Angular distance.
(see also: http://en.wikipedia.org/wiki/Cosine_similarity#Properties)
So if you want to take magnitude into account, you may actually be looking for Euclidean distance...
Let's look at squared Euclidean, for simplicity:
$$
\sum_i (a_i - b_i)^2 = \sum_i \left(a_i^2 - 2 a_i b_i + b_i\right)\\
= \sum_i a_i^2 + \sum_i b_i^2 - 2 \sum_i a_i b_i = ||A|| + ||B|| - 2 (A \cdot B)
$$
Now let's assume $||A||=||B||=1$, i.e. vectors standardized to unit length.
Then Euclidean distance is $\sqrt{2 - 2 (A\cdot B)}$!
In essence, Cosine similarity is like (squared) Euclidean distance after scaling each vector to unit length. I.e. if you have data that is very different in magnitude, but you do not want to take magnitude into account, then use cosine.
Note that angular similarity is scale invariant:
$$
\operatorname{CosSim}\left(\frac{A}{||A||}, \frac{B}{||B||}\right)
= \operatorname{CosSim}\left(A, B\right)
$$
And if I didn't screw up somewhere (please edit then!):
$$
\operatorname{Euclidean}\left(A,B\right)^2
= ||A||^2 + ||B||^2 - 2 ||A|| ||B|| \operatorname{CosSim}\left(A, B\right)
$$
(Law of Cosines).
Conversely, normalizing your data before using Euclidean yields:
$$
\operatorname{Euclidean}\left(\frac{A}{||A||}, \frac{B}{||B||}\right)^2
= 2\left[1 - \operatorname{CosSim}\left(A, B\right)\right]
$$
(Note that the right hand is a popular way of converting cosine similarity to a distance!)
And cosine similarity is monotone to squared Euclidean on the normalized vectors:
$$
\operatorname{CosSim}\left(A, B\right) =
1-\frac{1}{2}\operatorname{Euclidean}\left(\frac{A}{||A||}, \frac{B}{||B||}\right)^2
$$
As per @whuber's comment: the formula
$$
\operatorname{acos}\left[\operatorname{CosSim}\left(A, B\right)\right]
$$
yields the geodetic distance on the surface of the unit sphere to get from the point $A/||A||$ to the point $B/||B||$. For obvious reasons, the $0$ vector yields undefined results.
Typically, correlations are reported as the plain old $r$, i.e. directionality included. They are usually just reported in a correlation matrix without visualization. On occasion you will see scatterplots which can optionally be arranged in a matrix where all pairwise variable combinations are shown (see links below). Most often authors are interested in communicating a bigger idea, so correlations are only a stepping stone to the greater idea that they want to draw attention to.
That said, if the correlations are the most important part of your analysis, and you want to focus attention on them, then your graph is arguably appropriate. Keep in mind the primary purpose of a graph is to help make a point. By graphing $|r|$ you make it easy to visualize differences in magnitude. Just make sure you report the $r$ values in addition to the graph so all of the information is communicated to the reader. You don't want any misconceptions. If you are looking for something a bit fancier than a bar graph, check out the links below. Note that some of the more fancy figures add a line of fit to the data. Since you are using the value $r$, which is based on a linear relationship, you would probably want to use a straight line of fit if you did that.
Since you are making comparisons between correlations, you might consider reporting how they fit into effect size ranges, e.g. strong or weak, as well (see link below). And you can even test for significant differences between correlations.
For list of effect size ranges:
More typical scatterplots for multiple variables:
Fancy correlation figures:
Best Answer
Since your data matrices are symmetric, canonical correlation analysis(CCA) is not the right approach I think. CCA would look for linear combinations of distances that maximize correlations between the two sets. I would drop the correlation option.
The Procrustes distance may be a better option, since it measures the difference in shape of multidimensional ensembles. You could consider a resampling technique (such as the bootstrap) to test for significance, since I am not aware of any theoretical null distributions for the Procrustes distance.