If it's a 50% chance then neither is preferable, the only date format with an inherent superiority in any area is the ISO 8601 date format of YYYY-MM-DD H:i:s because it is computationally easy to sort in all cases by simple "higher or lower number" sorts and there is no ambiguity if you know the format. You can safely bet that almost no non-technical users are going to know the format by default unless their country happens to use it or a similar format.
The solution is to display the full name of the month in any written dates; "October 7th, 2011" can not be misinterpreted. When asking for a date input always state the format you're using near the field (e.g. MM-DD-YYYY).
To decide which format to actually pick, look at your domain. If it's a US domain (.us) or assumed to be a US domain (.com is often used as such for the big sites) some people may assume it's going to follow US conventions and in that case you may as well use US date format, as that's the best/only hint you're going to give. The same for .co.uk, ect. The only "best" here is what your users will most expect.
For related reasons the full 4 number year should always be used to help eliminate ambiguity, there's nothing worse than seeing 10/7/11 as a date format.