Hi @taylor,
Great question!
I’m guessing when you say the Tiller Monthly Budget you mean the Tiller Budget (that has a rollover column on the budget dashboard).
The major difference between the Tiller Budget and the Foundation Template is the rollover concept. Rollovers are like virtual savings accounts and make envelope or zero sum budgeting possible, if those are your preferred methods. It has a period interval of your choosing (weekly, bi-weekly, monthly) that is created automatically at the start of each period. You can also use these cool dynamic shortcuts to adjust your budgets or rollovers. It’s all powered by the Budgets History sheet (it’s hidden by default). Finally, it offers a savings goal tracking feature.
This template has some performance issues. It can run very slowly in the browser in some cases and sometimes the script that controls the period create fails and the period is missing requiring you to manually run that script.
The Foundation Template as a budget is way more simple to use, set up, maintain, and understand. It allows you to set up an annual budget starting with whatever month you choose on the Categories sheet. It doesn’t use heavy scripts so it’s a lot faster. It offers monthly and annual cash flow analysis and projections. It also includes an Insights sheet with quick spending and balance insights.
Because of the way these two budgets expect you to set budget amounts for categories they are incompatible with each other. The Foundation Template already has a budget in it, there isn’t a need for a second one. The Foundation Template was built off our “Tiller Monthly Budget” a distinct budget from which we adopted the Yearly Budget and Monthly View (now call Monthly Budget) tabs (even more tab name confusion, right 
?)
Finally, the major difference I’ve personally seen with customers is the level of complexity and learning curve to get started. The Tiller Budget, if you want to use the rollover or savings goal features is way more complex and has a higher learning curve and thus a greater time investment in understanding how it works. This is mostly because of the rollover and rollover adjustment concept.
The Tiller Budget template is supported in and by our community. The Foundation Template is supported by the CS team via support@tillerhq.com or the chat window.
Hopefully that is a comprehensive comparison that others will also find useful!
Let me know if you need any clarification.
Heather