In online advertising, recommender systems try to propose items from a list of products to potential customers according to their interests. Such systems have been increasingly deployed in E-commerce due to the rapid growth of information technology and availability of large datasets. The ever-increasing progress in the field of artificial intelligence has provided powerful tools for dealing with such real-life problems. Deep reinforcement learning (RL) that deploys deep neural networks as universal function approximators can be viewed as a valid approach for design and implementation of recommender systems. This paper provides a comparative study between value-based and policy-based deep RL algorithms for designing recommender systems for online advertising. The RecoGym environment is adopted for training these RL-based recommender systems, where the long short term memory (LSTM) is deployed to build value and policy networks in these two approaches, respectively. LSTM is used to take account of the key role that order plays in the sequence of item observations by users. The designed recommender systems aim at maximising the click-through rate (CTR) for the recommended items. Finally, guidelines are provided for choosing proper RL algorithms for different scenarios that the recommender system is expected to handle.