Thanks for the qualification. So it's 5 all in major trophy wins and it is your criteria for basing your statement. Some feel the Scottish Cup holds more value than the League Cup, but for me, it takes the same effort against basically the same standard of opposition to win either. Should one hold more significance than the other? It certainly didn't when we, the Shed, lifted our first major at Dens and then our second the following year.
If your limited criteria is all you are basing 'most successful team' upon then hold onto your hat and proudly head off into the sunset. In debates such as this, few are content with a draw based upon limited criteria and seek other factors to prove their point. Here is a good start, which should interest you since the first section sort of supports your argument.
https://en.wikipedia.org/wiki/Dundee_derby