I am not sure you really have a choice do you? Seldom have I seen projects like that where you can chose to include or exclude materials, but if you have the choice I would let them provide materials. It surprises me sometimes when this happens, because while the owner wants to get the lowest price and if they have the ability to buy materials at wholesale it can save them money. However if there is a problem with defective materials, they end up getting involved with trying to determine if the install or the product was defective. If a fire hydrant is found to be defective the owner will end up fighting with the supplier and paying at least up front for the redo. Doesn't take long for any savings in material mark up to disappear. Doesn't happen often but I have seen it with waterline that was defective from the factory causing all sorts heartache. I don't think it is worth it for most owners to involve themselves to that degree. Especially if they mandate the contractor supplies materials and install. Makes it pretty clean if there is an issue. Its your problem to deal with as the contractor. But if they are willing to "get into mud" let them take a portion of the liability.
The money made off materials on competitively bid jobs most often doesn't amount to much in my view, especially as mentioned above by the time you sit on the costs, manage theft and so forth. If owners supplies materials, write the bid so that materials are transported by the supplier to the job and you don't have to mob it yourself or incorporate that time in with your mobilization costs. Everyone will have to account for the same time so it should competitive.