Basically an envelope budgeter will save you money, the others will tell you what money you've spent after you've spent it, which is usually too late.
I'm not sure which category I'm in
I've been using MS Money since 1.0 and spreadsheets before that. I do use budgeting, but not in the sense that I only have a fixed amount to spend on any particular category in any month. It doesn't matter if the actual amount is under or over the budget. What I use budgeting for is for predicting future cashflow in all my accounts. The cashflow forecast is absolutely essential for me and budgets are necessary to make it work.
Maybe I should explain what I mean - I would love to hear that there is another application which is able to do this. The key elements are:
1. Recurring future payments and deposits with flexible payment intervals and dates, and the ability to edit an individual future transaction for a specific date without affecting other payments in the future, and the ability to enter one-off future transactions.
2. Budget for each category which can be set up manually, or automatically based on a combination of historical spending patterns and future recurring payments, and which can be allocated to a specific account or split over multiple accounts e.g. dining out always on Visa, supermarket always on Switch card, fuel on either account.
3. Intelligent cashflow forecast for each account for up to 12 months ahead, which takes into account all future payments and deposits, budgetary amounts, and any actual transactions recorded in the period e.g. say the average spend on dining out is £200 a month, we are halfway through the month and have spent only £50, and there's a recurring payment on the last weekend of the month for £60, cashflow forecast would assume that another £90 will be spent in this category this month.
This is all a lot simpler than it sounds but in practice, I know roughly how much I will have in any one of my accounts up to 12 months ahead. I also know what my credit card bill will be every month for the next year, can adjust the future payments individually from my cheque account to reflect that, and so I know how much can be paid into my savings account every month for the next 12 months. Obviously this is just a forecast but getting the budgets right makes it a pretty accurate one. Additional expenditure which is unplanned makes you think about the whole picture of the next 12 months - not just a month at a time.
Exceeding a budget for a category in a month happens frequently and the idea of a tipping bucket or an envelope or whatever maybe doesn't fit with that. In my system, the budget is an average monthly spend, not a maximum, so some months it will be over, some under. Over all the different categories it evens out. But my point is the budget is not a budget in a strict sense of some arbitrary limit to spend on a category beyond which there's a problem - it's a means of forecasting only.
This is not something I am ever going to give up - it works very well as a system and if I have to keep using MS Money in a virtual machine for the foreseeable future, then I will do that. However I would love to hear that there is a native Mac app that will do the same things for me. Is there? I have looked at a the websites of a few apps and come to the conclusion that there isn't

I'm wondering if I'm going to have to write one myself in the longer term.
I should also say that really, requirement number 4 is an easy import directly from the .mny file. I can't believe it would be that hard to reverse engineer the format and take care of all accounts, categories, budgets etc in one go. QIF export/import is not a very flexible or comprehensive medium - and who wants to do it one account at a time? How does that even work if you have lots of historical transfers between accounts. I'm wondering if the next version of Quicken will do exactly that. I'm sure I read when MS killed Money that the next version of Quicken was going to be delayed due to conversations with MS to make the transition easier. I read that as suggesting MS are going to document the format of the database file and allow Quicken to maybe import directly from the .mny file. I hope so.