This must be hypothetical because there is no DH for real baseball-NL.
You state that pitching is equal. On paper, sure, but it doesn't translate that way when games are played. As the saying goes, "momentum is only as good as tomorrow's starting pitcher".
In your scenario, most everything being equal, defense would probably win in seven games.
One of the beautiful aspects of sport is that it is all live, and anything can happen.
Ep and I could make it happen!
I'm not on First, Who Cares is on Second and Nobody is on Third ! ( Oh and on the DH question: most pitchers couldn't hit a bull in the butt with a Base-Fiddle !!! ) ( Therefore we need the DH in both leagues lol ). 
I would say whichever team can get on base more often and take more pitches to wear out the opposing starters to get to bullpen quicker.
I would say whichever team can get on base more often and take more pitches to wear out the opposing starters to get to bullpen quicker.
That's a good point, and I think a hit and run team would have more disciplined hitters.
Who knows what happens since you only vaguely described the teams. There are so many variables we don't know, like how good is thier fielding or coaching.
I suspect you want us to choose between power and speed. It depends on how good the the power hitters are versus how good the other players are. There are 5 category power hitters and then there are guys that barely keep above the Medoza line but can belt 35 taters a year.
To answer you question as well I would care to, I'll just say I'm an adherent of the Earl Weaver (longtime Orioles manager if you are not familiar) school which says you win with "pitching and 3 run homers".
BTW, the National League is Senior Circuit since they started in 1880's and the American League is the Junior Circuit since it started in the 20th century, 1903 if I remember correctly. Your description was a little confusing.
National League: 1876
American League: 1901
I was wrong. I intentionally left many traits of the teams undefined in order to provide lattitude in responses.
This must be hypothetical because there is no DH for real baseball-NL.
You state that pitching is equal. On paper, sure, but it doesn't translate that way when games are played. As the saying goes, "momentum is only as good as tomorrow's starting pitcher".
In your scenario, most everything being equal, defense and three run homers would probably win in seven games.
One of the beautiful aspects of sport is that it is all live, and anything can happen.
Ha! He thinks he's Earl Weaver. The obvious winner would be the Tigers.
And it's year in year out with discipline and a base level of talent.
Just noticed that you called the AL the senior league in the opening post. I don't think Nap' would agree with that.
AL Central rules. Records in the last ten games:
Tigers 9-1
Indians 9-1
Royals 9-1
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Let's say there's an American League team and a National League team that have equally good pitching. Let's say the senior league is loaded with home run hitters. They have a DH specifically for this. Their weakness is that they strike out a lot.
Let us further assert that the National League team has a true lead off hitter, guys who know how to get on base, bunt and steal. Their weakness is that they have only one or two guys who have hit one out of the park since Little League. Who wins a 7 game series? And for all you smart asses out there, let me beat you to the punch: it sure won't be the Cubs!