Test dispersion around $y = x$ line 
As shown in the figure, the lines in both panels are $y = x$. The lines are not regression lines. I see that in the right panel the data points scatter further away from the $y = x$ line. Abundance.y and Abundance.x are supposed to be the same so that they should gather close around $y =x$ line. We are testing whether the left panel points are "tighter" around $y = x$ than the right panel points.
What is a good test for this? 
 A: Concordance correlation measures agreement, i.e. quantifies how far $y = x$, rather than how far $y = a + bx$. The idea is most often associated with Lin, but was earlier discussed at least by Mielke and Krippendorff. 
More at 
Does concordance correlation require data to be normally distributed?
Does the concordance correlation coefficient make linearity or monotone assumptions?
A: Have you heard about Bland-Altman methodology ? I assume your data is paired given the graph you make.
By computing a classical prediction interval on the data difference $X=(Abundance.y - Abundance.x)$, for each of your graph, you can simply compare which interval is the smallest. You can also see if there is a discrepancy from the reference line by looking if the difference is close to 0, parallel to the 0 horizontal reference line, or not.
Here is the prediction interval (assuming your Bland-Altman plot is "horizontally shaped": $$\overline{X}_n\pm T_a {s}_n\sqrt{1+(1/n)}$$
But please don't look at determination coefficient $R^2$ !!
