As per my understanding, you want to fit a linear regression model, however, the two datasets you are using have different variables.
One way to overcome this would be to see if there is an appropriate value, such as zero, which can be added to missing variables in both datasets. However, this might only make sense if only few variables are different. If all variables are different, then it might not make much sense.
On the other hand, if you're issue is that the observations are not for same stocks, then it might not be useful to compare them, assuming they are independent variables. If you want to test the hypothesis that they are somehow related, then you need to check the relationship between the two sets of variables. You could do this by predicting the after variables based on the before variables.