In: Economics
The question is highly subjective. Like it is mentioned in the question only, some claim that the future of advertising lies in online mode whereas TV advertising supporters tend to disagree. This in itself shows that the question requires one's personal views and that there is no strictly right or wrong answer. However, as a contribution to the discourse here is my answer:
Economics in very basic form is defined by the decision making of a household. The whole economy, processes, markets, transactions are ultimately a result of how the household/consumer reacts, the decision he takes and the choices he makes. Advertising is practically a method of trying to influence the household's decision. And this is evident, what the consumer sees more, stays in his head and is more like to pose an influence. So, the future of advertising does not deoend upon online mode or TV per se but on the future of these two itself. TV currently has a wider user base spread over greater time span in terms of usage. However, lately people have started to shift to online spaces for a better proportion of their time than before, . If in future, online space takes over the TV space in terms of time period, then no wonder advertising's future shall lie in that else TV will remain unsurpassed in that field.