I wouldn't say you need a discerning palate - if your experience with sushi is anything from US sushi buffets to even mid-scale sushi full service restaurants in the US, you'll notice the difference right away. What I do suggest, in order to get the best experience and understanding, is to read about Jiro, understand the difference between 'typical' sushi and edomae style, read up on the different rice types and preparations for sushi, and then you'll understand more about what you're eating and what makes it special.

Taste-wise, you'll notice the difference right away - from the texture and flavor of the rice to the freshness and distinctive taste of the fish, you'll realize this is way different than what you've likely had before. You can find great tasting fresh fish pretty much anywhere in Japan - the reason to try Jiro is to experience the creations of a man who has dedicated his entire adult life to the continuous pursuit of perfecting one single thing and has taught others how to replicate his skill and passion. You just won't find that sort of perfection with any other chef and I believe it's worth experiencing.

I would try to get a reservation at Ginza for dinner or lunch (the menu is basically the same for either, as is the price) as I believe it's worthwhile to be served by Jiro himself before he retires, but if you cannot, then visit Roppongi and splurge for the sashimi service.