Ok first off, I have to say in my experience and area wakes and funerals are not even remotely similar. Its not something you can say "I'm going to the wake/funeral" about. They are very very very different things, in different places, on different days. (Similar to a "wake" would be a viewing or shiva.) You might go to both the wake and the funeral, or just one, but they are not interchangeable words. In my area, the wake, and perhaps the funeral church/temple service is for extended friends & such and the actual funeral (burial) is only for those very close to the departed. The difference in attendance can be 100's of people with way more at the first and very few at the latter.
Either way, food wouldn't be brought to either unless its in the family home (like a shiva). The food is something geographically close friends & family bring around the family home in the days after the death (ranging from 1 day to a month later). Sometime people will send food (like a fruit basket) to the home, but be careful to not send it on days the family will be out all day at the funeral home or the cemetery attending to the formalities of the death. The point of the food is an either or thing - sometimes its because the grieving family will be having lots of people over the house - out of town relatives in for the services, friends & neighbors dropping by to pay respects/check in, etc and this way the family has food in the house to offer them, and sometimes its to ease the burden of having to shop and cook from themselves during their mourning period. As such the food an be a fruit basket, a box of chocolates, a frozen casserole, a cold cut platter, an assortment of various ready to eat grocery type foods, etc depending on when its being given and its intent.