As I am sure has been outlined above, Mint and YNAB are very different tools.
Mint is great if you want to get a sense of where your money is going. How much is going to your groceries, or specific grocer? How much are you spending on this or that other thing? Mint is a great tool for getting that snap shot and see trends over time. Mint, for the most part, answers the question where does my money go?
YNAB is almost the inverse. YNAB helps you decide how much money gets spent where. How much of your pay cheque do you need to devote to electric, water, gas. How much do you want to set aside for meals out, or divert to a specific savings goal? YNAB, for the most part, answers the question where do I want to spend my money?
Now, they can actually work together. In YNAB, whenever you get money (e.g., a paycheque), you allot that money to a specific job (groceries, car repairs, saving up for a new iPad, etc). But how much do you spend per month (or week, or two weeks) on groceries? Ideally in YNAB you’re budgeting approximately the amount you’re likely to spend between now and your next paycheque, but most of us have no idea what that amount actually is. I know we didn’t. We under-budgeted by at least $200 for the first month of using YNAB. But, if you’ve been using Mint, it’s easy enough to just have it spit out a report for much you spent on groceries for a given period. BAM, a rough starting point for your groceries budget in YNAB!