Dundee have exactly the same amount of major honours as United, including the top league as you point out. Therefore are not more successful than us.
Two of your reasons is that they have made more money in out going transfer and have a slightly higher match day attendance? Fairly clutching there chief. With Dens highest attendance being 43,000 and Tannadump's being 28,000, that probably evens your flying Unicorn stats out.
Who hasn't beaten Barca? In fact Dundee were the first club from outside Spain to beat both Barcelona and Real Madrid at their home grounds. We have also got a perfect home record against AC Milan, but they are shite of course.
"I'm just cherry picking facts here but it's hard to find an argument that Dundee FC can better that."
We have won 344 more league games than United. But I won't use this fact as I see as as pretty equal over history, as these records will never change or have a time limit on.