Compare Classification Performance in Datasets drawn from Different Populations I've read some classics about comparison of ML Algorithms i.e.

Dietterich, T. G. (1997). Statistical Tests for Comparing Supervised Classication Learning Algorithms 1 Introduction. Science, 10(7), 1–24. Retrieved from http://dx.doi.org/10.1162/089976698300017197


However I feel totally lost about a specific problem.
Backgrond / Status Quo
I have two dataset ($N_1=552$, $N_2=543$) drawn from different populations. 
 Both contain the same set of features and the same criterion (7 class labels).To simplify I will spare the details on preprocessing and hyperparameter tuning.
In the end I have two trained algorithms (i.e. two RandomForests:  $RF_1$ &amp; $RF_2$) for both datasets ($df_1$ &amp; $df_2$) respectively 
Goal / Aim
I want to know if it is better to train the algorithm using data drawn from population 1 and evaluate it using data drawn from population 2, or if the opposite is true. So which population generalizes better to the respective other. To be more precise if a measure of the classification performance (i.e. Accuracy or Kappa) for the $RF_1$ (Random Forest trained in dataset 1) tested in $df_2$ is significantly higher (not caused by chance) than the performance for the $RF_2$ (Random Forest trained in dataset 2) tested in $df_1$. 

$Acc(RF_1-&gt;df_2) &gt;  Acc(RF_2-&gt;df_1)$

Question
Is there an apropriate test for that? Is it as simple as the $\chi^2$ or a exact binominal test?

Edit  
Or am I comparing apples and oranges, and there is no way one could compare this two classification results? I am very thankful for any direction you can give me.
I understood it wrong ,here is the paper which discuss using multiple data set for the same classifier-

http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.141.3142&amp;rep=rep1&amp;type=pdf

They conclude- 
"
We theoretically and empirically analyzed three families of statistical tests that can be used for
comparing two or more classifiers over multiple data sets: parametric tests (the paired t-test and
ANOVA), non-parametric tests (the Wilcoxon and the Friedman test) and the non-parametric test
that assumes no commensurability of the results (sign test). In the theoretical part, we specifically
discussed the possible violations of the tests’ assumptions by a typical machine learning data. Based
on the well known statistical properties of the tests and our knowledge of the machine learning data,
we concluded that the non-parametric tests should be preferred over the parametric ones."


I recently learned about 5x2cv paired t test procedure to compare the performance of two models.

Please refer below-

http://rasbt.github.io/mlxtend/user_guide/evaluate/paired_ttest_5x2cv/

It Implements the 5x2cv paired t test proposed by Dieterrich (1998) to compare the performance of two models.