Pearson and Spearman correlations - how to determine if they are "similar"? I would like to know if there are any rules to determine if Pearson's r correlation values are similar to Spearman's rho?
For example, if r = -.207 and rho = -.282, are these similar enough to just report r? 
 A: In case of large sample sizes, the significance test is the same for both indexes:
$t = \sqrt{\frac{(n-2)}{(1-r^2)}}$
So you can generally treat both indexes the same way and test their difference for significance. 
However, things might be a bit complicated, as they are non-independent correlations (i.e., both are derived from the same sample). There have been articles by Steiger (1980, [1]) and Meng et al. (1992, [2]) which treat this issue. In the cases covered there, however, it is always a correlation between one variable $x$ and two other variables $y$ and $z$ (i.e., comparing $r_{xy}$ with $r_{xz}$), which is not exactly your case.
[1] Steiger, J. H. (1980). Tests for comparing elements of a correlation matrix. Psychological Bulletin, 87, 245-251.
[2] Meng, X. L., Rosenthal, R., & Rubin, D. B. (1992). Comparing correlated correlation coefficients. Psychological Bulletin, 111, 172-175.
A: Because Spearman rho is the same formula as Pearson r, only applied to ranked rather than to raw data, the two coefficients can and may be directly compared in magnitude. (In contrast, for example you cannot directly compare Spearman and Kendall correlations.). So, in your case, as -.282 is somewhat greater then -.207, you could conclude that the "true" association between the variables is not so much linear but rather monotonic.
See this for more particulars.
