chemical responses last longer than nervous responses
JPW's answer covers most of the relevant points. I would interpret your Q in a slightly broader scope in that chemical responses technically should not be confined to hormonal ones. One could argue that responses of the body to changes in oxygen concentrations, H+ and OH- ions [so acid-base status] as well as chemotactic responses whereby certain inflammatory cells are attracted to sites where they are needed via the action of cytokines can also fall under the classification of chemical mediators. Other chemicals with important physiological/homeostatic functions include the prostaglandins with their crucial role in the maintenance of temperature [and of course, our human intervention in the use of drugs that block cyclo-oxygenase e.g. ibuprofen to treat pain and pyrexia].
Hormones are exclusively either proteins e.g. the 51 amino acid polypeptide insulin (broken off from the 86 a.a. pro-insulin) OR steroids e.g. the adrenal cortical hormones and the sex hormones. The substances mentioned in italics above are heterogeneous in chemical composition - having said all this, JPW's analysis of hormonal action also for the most part applies to these other chemical responses, except perhaps in certain instances of allergic reaction (Type I or immediate-type hypersensitivity reaction) where an anaphylactic reaction brought about by chemical agents such as histamine and arachidonic acid in conjunction with IgE can spark off a very quick and as it happens, quite catastrophic set of events, sometimes fatal. (Admittedly, this does not fit your title of homeostasis).