I am going to buy a BBQ and I am torn between a cast iron BBQ and a stainless steel BBQ. What are the advantages and downsides of each?
Assuming you are talking about different types of grill grates:
In general, cast-iron gives you better heat retention (flip-side: slower preheating) and better non-stick behavior if well seasoned. However maintenance with cast-iron can be a bit of a hassle. You have to develop and maintain seasoning and also take precautions against rust.
Stainless steel does not rust and is easier to maintain, however it is less non-stick and won't give you the same grill marks that you get with cast-iron.
Ceramic coated cast-iron is supposed to be a good compromise, however, I really hated the ones I had as they were very hard to clean and the coating eventually cracked, rusted AND chipped off.
tl;dr - If you are willing to put in the maintenance, cast-iron is generally the superior choice. If you aren't, go for high quality stainless steel grates (like these) -- you won't be missing all that much.
See also the answer to a similar question I had regarding a choice between porcelain and stainless steel:
(I went with stainless and have been happy with the performance)