It depends on so many things that it’s hard to answer this question without accounting for everyone’s individual scenarios.
The things to consider are:
How long will I be in this house?
Is any of my debt at a low 30 year fixed rate (like student loans)?
Is any of my debt currently deferred (like promotional plans or student loans)?
Do I have a history of running up my balances when I have credit available?
Is my house likely to appreciate or depreciate?
Do I have a history of earning good rates of return on investments?
And many other questions.
There is one overriding principal to keep in mind though. Wherever you put the money, don’t spend it twice. So if you you pay off credit cards and do 100% loan, you’ll then have access to credit cards. If you know you have bad credit habits, you might run the risk of borrowing against those cards again and having more debt than you want. On the other hand, a larger portion of your total debt would be tax deductible.
If, however, you go the large down payment route and leave your debt, it’s harder to get access to that money again if you have an emergency. But it will keep you from spending money you think you might be tempted to spend.
The more conservative choice is to go with the down payment, UNLESS, you have a proven history of managing money well and adding to investments. So there is no wrong answer as long as you don’t use it to create more debt for yourself.
If you’re credit cards are at 9-20% and your mortgage will be around 7%, it’s a pretty clear-cut choice, and you only have to weigh the discipline factor. If your debt is a student loan at 4% fixed for 25 years, you’ll be better off leaving it in place. Consider immediate future cash flow and long term interest paid and make your decision according to your personal preference.