Econometric question?

Only one thing for sure from your information is that the second equation has more independent variables than the first one.But more variables cannot be justified as good or better in econometrics. You should run the two equations and make a test using conventional testing methods such as F-test,R*2,t-test,Durbin-Watson test, to justify which equation yield better relationship.But from your specification,I would go for the first equation using only one dummy variable to separate Canadian from US firms.In the second equation,there is a risk that the last two variables will create multicollinearity which will affect your parameter estimation.