I think any answer needs to be qualified, because we are not talking apples to apples here.
Leafs have been around forever. Have not won a cup since 1967, before I was even born, and I am in my fifties. San Jose has been around since, when...1990 or so? I remember getting hockey cards of early Sharks players in high school, so probably around that time.
The fanbase for the Leafs, as well as the media market for the same, is significantly larger than San Jose and with that comes different expectations. Fairly or not, choking under greater expectations is worse, at least on a perception level.
That said, San Jose, while equal to the Leafs in not winning the cup, have exceeded the Leafs insofar as their playoff performance. They have gone deep in the playoffs a number of times and I think even made the Finals. One can say well, they didn't win anything so same difference and that may be right, but (to me, anyways) choking in the midst of relatively moderate success seems to be better than choking in the midst of relatively little to no success. The Leafs have also had more recent memory chokes, some of which have been more than memorable. My adult son still remembers us watching that Leafs/Bruins game where the Leafs had a lead in the third and then lost the game and the series. I think part of the reason why he remembers that so well is due to the immense pressure and coverage and fairly or not, the constant media conditioning that this may indeed be the Leafs' year. Hence, my earlier comment about expectations.