Although it's hard to compare a team to the grandfather of the modern day NFL offense. The comparison is there. If you just look at it as The Rams spread everybody out and put up a bunch of points.. sure that's not how this Cowboys team is built. But the Cowboys are every bit as balanced as that 01 Rams squad on the offensive end, here are some other comparisons.
Both teams have strong QB/WR play but win their ball games based on the RB. As an effect they can both beat you multiple ways on the offensive end.
Speaking of the RB, both teams were owners of the best back in the league.
Both QB's were no name undrafted guys who became stars in the league.
Both teams have questionable play from their Defensive unit.
Both teams amassed 6 game win streaks right out the gates. Both teams finished the season winning out and heading into the playoffs the team to beat.
Now you got a point with the 07 Patriots. There is no comparison with the Cowboys. They had a good D. And their whole demeanor that year was we are out to embarrass the entire league. I put that team on a whole other level. I think only 2013 Denver comes close recently and they didn't have the D to match 07 New England.