The Cardinals do not have the most wins in the National League. That distinction belongs to the Los Angeles Dodgers who are 16-11. The Cardinals are 15-9. Those nine losses, however, are the fewest in the National League, which gives the Cardinals the best win percentage among those teams at .625. Going by record, the Cardinals are (currently) the best team in the National League.
Record does not paint an accurate picture though. There are many factors that can go into record like strength of schedule (though the Cardinals have faced some tough competition so far) and home/road splits (the Cardinals are 5-6 on the road — five of those losses were at Miller Park — and 10-3 at home).