Two Cups without even batting an eye. Project this over 50 years, and you get one team with tons of Finals appearances, but only 5 Cup wins - would almost give them a choker label. The other team would have to live with a reputation of major "suckitude", but would have still been able to close the deal an amazing 10 times - in a 30+ team league, this would be an amazing kill ratio.
The team with the 10 Cups would resemble something like the Penguins. They suck for a long time, and then they string a couple of Cups together because of awesome draft luck. I see the team with the 5 Cups as more of a Flyers or a Bruins. Consistently better every year, but with fewer Cups to show for it over the same time period.
At the end of the day, when you look up into the rafters, it's not how many banners you have (Presiden't Trophy, ECF/WCF Champs, Stanley Cups, etc), it really only is about how many Stanley Cup banners you have.