Baseball Regression Issue (STATA)


I am glad a site exists like this where peole can compare information on this growing field. Baseball analytics is huge these days and I am doing some research on the field myself. Using STATA, I regressed my dependent variable (runs scored by Home team) on 10 independent offensive variables (hits, homeruns, walks, etc) over 4500+ games, and did another regression for Visiting teams. My R-squared values .885 and .894 for home/visiting teams (respectively) are encouraging, but I dont want to stop there.

Is there a method of comparing the differences between these two regressions in order to determine if any of my independent variables are more important for a Home/Visiting Team?
Example: coefficient for hits in a game: Home=.885 Visiting=.894
and all p-values are zero except for strikeouts, and this is still below .05.

Amy way to determine if some of these independent variables are better predictors of runs scored for either the HOME or VISITING team? Thanks for reading.