I run a disaster relief operation, and we are building a relief site
outside of New Orleans in Plaquemines Parish.
We want to know what the difference in cost is between buying a
generator and constantly filling it with diesel is vs. paying for
electricity from the local electric company? We are talking about a
175kw generator, and we are in south Louisiana - just a ballpark
answer is fine, as we don't know the exact gas prices and electric
prices.

It appears you are considering either one or the other.  The ideal
would be on the grid and the generator as backup.

It's always going to be cheaper to buy electricity off the grid.

How long you expect to be off grid will be important.

Casinos (Indian and otherwise) usually have backup power just sitting
around waiting for a power failure. They can not afford the slot
machines to go dark.
Maybe you can arrange some sort of sharing arangemnt with one or two of them.
They can always use good publicity. Somrthing on a trailer maybe.