This paper analyzes a two-sided market model in which platforms compete for advertisers and users. Platforms are differentiated from the users' perspective but are homogenous for advertisers. We show that, although there is Bertrand competition for advertisers, platforms obtain positive margins in the advertising market. In addition, platforms' profits can increase in the users' nuisance costs of advertising. As a general insight, we obtain that factors affecting competition in the user market in a well-known direction without externalities now have opposing effects due to competition in the advertiser market. The model can also explain why private TV platforms benefit if their public rivals are regulated to advertise less - a result at odds with models in which there is no competition for advertisers.