Hi ^_^.As far as I know,
* 'expense' is the amount of money you spend on something
or spend for a particular purpose (in this case, it is 'expenses')
I bought this car at great expense
Legal expenses, medical expenses..
*'expenditure'
also means' the amount of money' but is often used for something quite important or a quite large budget, and often public such as' public/military/eduaction expenditure'. I have never seen such phrases as' military expenses'
It also has a second meaning: the act of using/spending money, time, energy, material..
*To conclude I think 'expenditure' is applied while mentioning 'public' money and expense is used when refers to an amount of money used for individual purpose.