Lets assume one has 2 datasets: with different number of rows (samples) and columns (features). Each of these 2 datasets have a column as a binary response variable. Lets say healthy or not. What sort of statistical methods can be used to help us for better feature selection results, or better performance in classification models, utilizing both datasets?
Put them together, call them a single dataset, add a column indicating which dataset they came from if that represents something meaningful you can measure out of sample (location?), proceed as normal with multiple imputation or another technique to deal with all the missing data this generates.