I have used Quicken (but not the current version, so my comparisons may be old/no longer accurate). Quicken was about understanding what you spent. YNAB is about identifying how you are going to spend every dollar you have right now. I have used YNAB for 3 years now (at $50 a year), and have found it is much better for me than Quicken ever was at being sure I am saving for future large expenses like property tax, Car insurance etc. I know how much money I have set aside for each major category, and how much more I need in each category and by what time. I'm not always as clear how much I have in each account, except when I reconcile my accounts each week. Quicken gave me great visibility into each account, and I was very clear how much I had available in each balance.
For me, I like the categories that tell me how much I have to spend on x, and if I go over that, big red warning signs go off telling me I've overspent and have to move money around. I never got that with Quicken. I'm not sure if it is worth it to me to keep going on YNAB with the price change. We'll see I guess.